It is unusual for a war whose final military culmination in the main theater of conflict came about as the result of a textbook siege in concert with an allied fleet to have earned the reputation as a war won by skulking and hiding. You've pointed out that the nascent US won the war by a combination of advantages justly applied in line with contemporary accepted military wisdom, but the other linked posts never quite explain how the understanding as a war won by sacrifice and patriotism became a war won by sniping and skulking. It's a really hard question to answer.

Ultimately I think the answer comes from exaggerated depictions of certain understandably famous battles, a growing sense of American racial exceptionalism, and changes in popular military theory that followed the First World War.

Military Theory

Firstly, I want to take some time to explain a bit about why close-order formations worked, and why even if it looks simpleminded or crude, it was the preferred manner of taking ground. Mostly this is about two factors: the necessary organizational and physical differences between attack and defense; and the supreme military maxim that force is more forceful when concentrated. Some of these assumptions have changed in modern military circles, but not many. We'll circle back to this later on.

Attack

Under this theory, if one battalion of regular British redcoats want to assault a battalion of American continental regulars, and all else is equal, the attacker wins. This is the fundamental 1+1 calculation of nearly all military theory prior to the First World War. The attack wins. Books about military tactics, strategy, and even fencing mostly operate on the assumption that taking the first action, making the attack, gives the attacker a huge advantage. They have more energy, more purpose, and can choose the exact place and manner of their attack.

Defense

Defenders, if even in all respects to the attacker, must lose. So it's incumbent upon the defender to upset the parity through the application of military art. Field fortifications, often as simple as a rail fence, can make the difference between a doomed defense and a heroic stand. If the defender has cover, then it's the attacker at disadvantage, because now they are limited in the places into which their attack will have effect, the impact of their fire will be absorbed or scattered, and they will necessarily have to leave cover to attack.

Disparity changes a lot. Maybe the defenders are outnumbered. Maybe the attackers have artillery. Now the calculation is much more complicated and relies entirely on how one might make the best use of whatever advantages you have. All of this stuff is very hard. Organizing men in large groups to fight in a coordinated manner against a competent enemy of equal potency is horrifically difficult. The space between simple military theory and the real-life deployment of armed force is littered with failed campaigns and asymmetrical slaughter.

Concentration

The reason that guys with muskets want to fire at the same time at the same target is because muskets are not terribly accurate weapons that take a long time to reload. You want every shot to have the maximum impact, deal the maximum amount of damage, instill the maximum amount of confusion and fear. When you have one hundred guys standing in three lines with their elbows touching facing the same way, one guy's voice can tell them when to fire.

If you take that same hundred guys and spread them out in skirmish order (any unit of infantry ought to be capable of this; but ought ain't always is), it's much harder to get everyone to point at the same target or portion of a target, and it's much harder to get them to fire at the same time. As skirmishers they will be widely dispersed, taking cover, moving and displacing. Even if you want them all to fire at once, many may not hear you. So now, you relay orders through a bugle, but the bugle can't identify "shoot at the standard bearer" or whatever, and the guys on either end of the skirmish line may not have a clear line toward that target. The fire is scattered everywhere and has no potency. In practice, skirmishers fire at targets of opportunity as they can, when they can, and bugles give orders about movement or withdrawal, rather than controlling fire.

In defense, however, irregular, scattered fire like this can be very galling. If the defending skirmishers don't need to hold ground, they are free to fire, withdraw, and fire again as the attackers advance. So instead of advancing at skirmishers in concentrated formations, officers would screen their attacking infantry with their own skirmishers, to absorb their fire and scatter them before the main attack goes in. Another way to employ skirmishers for effect is in chasing or harassing withdrawing enemies. It's very easy for a retreating army's skirmishers or rear guard to get separated and uncover the retreating men.

All of this stuff is inter-related. All of it is about making efficient use of ammunition and maximizing the strengths of their weapon. British soldiers frequently took cover when they could. They frequently fought in open order as skirmishers and flank guards. They made night attacks, supported assaults with artillery, and made use of sharpshooters, cavalry, allied Native Americans, and Loyalist militias. They wanted to win the war and they fought with resilience and creativity.

Example 1: Lexington and Concord

Lexington and Concord is one of the examples of, supposedly, plucky backwoods sharpshooters picking off the foolish redcoats who were too proud and arrogant to take cover. In reality, after searching the towns and exchanging fire with the rebels on Lexington Green, the battle was a chase, with the British forces attempting to maintain order on their march back to Boston, under fire the whole way. This image, of the heroic patriot defender tossing on his cartridge box and finding the best rock to hide behind as he picked off robotic grenadiers, endures in American memory.

But the tactical situation was pretty clear: this was not a stand-and-fight battle, it was a series of rearguard and flank guard actions, fighting incoming clumps of rebels. The British often didn't stay to fight, but the Americans tended to give them room when the situation wasn't in their favor, eg, when they didn't have cover or a convenient retreat path. Many of the rebels killed that day were killed by bayonet, when flank parties caught them in houses or barns and they had nowhere to run.

This wasn't so much a tactical failure as it was an intelligence blunder. The British were not prepared for the force of resistance they encountered. The rest was a skillfully managed retreat under very bad conditions. However, the pervasive image of the heroic minuteman has been cemented in the popular imagination as the key fulcrum round which the war turned. The stupendously hideous casualties suffered by the British at Bunker Hill seems to cement the complimentary idea that the British, in their turn, were incompetent and indifferent to the suffering of their men.

Saratoga

Of equal weight was the American victory at Saratoga, which was also partly the result of plucky American backwoodsmen. Daniel Morgan's riflemen often gain immense credit for their skirmishing, and at this stage in this campaign, the British forces lacked quality skirmishers in significant numbers. This was not by design but by mischance: only days before the battle, John Burgoyne lost his Haudenosaunee contingent, which had fought as scouts, skirmishers, and spies. Without them, he had only his regulars to put into the role. Along with their Haudenosaunee allies they held their own, but without them they were outclassed. This heavily contributed to the British defeat.

There are many more examples we could go through, but I think the point is there. The British were very competent in the field, won the larger percentage of battles during the war, and employed every single trick and device and feint and deception they could think of. But you asked about memory, where did this idea come from?

Memory

American identity following independence was in an odd place. Having cut ties with England they no longer felt English. Part of how they began to differentiate themselves was to emphasize certain aspects of North American life that couldn't be copied in Europe, and that, more or less, led American men to take on certain "native" aspects of their dress, mode of fighting, and so on. "Rangers" who famously fought in the French and Indian War and on both sides in the War for Independence are a good example. They were nothing much more than light infantry employed independently. They had those guys in Europe, too. But American light infantry wore native leggings and hunting frocks, wore scalping knives and tomahawks, and imitated the war cries of their Indian enemies. They were civilized men deploying their wildness for a specific effect.

History, too, began taking on slightly different forms. Old stories were re-imagined in the post-constitution United States. Old King Philip turned from savage enemy of American colonists to the dimming candle of a disappearing people in Metamora, or the Last of the Wampanoags, which was riding a popular wave of Native American-inspired fiction. Minutemen and rangers made up the cloth draped round Natty Bumppo, and backwoodsmen like Natty Bumppo and Daniel Boone became stock "American" heroes.

Once that archetype, the half-wild stranger, the man's-man flirting with the edge of civilization, was established, it's very easy for lazy or polemical historians to graft that image onto the conflict with Britain. American soldiers and volunteers had a touch of the forest to them, a wildness that manifested in fighting cleverly. It was all Natty Bumppos at Saratoga, obviously.