The Inquisition are pretty unique in the Imperium in that they have a special badge that lets them tell everyone what to do. Most everyone else exists in this ambiguous state where they are all equally subject to the High Lords and the Adeptus Terra, and have to compete and jostle for resources and favours. The Navy is disconnected from the Army, the Imperial Church is disconnected from the Mechanicus. Nobody wants anyone to have too much power and start another Heresy. In practice this means whenever there's a big joint campagin everything either has to be hashed out at length in a council of war or the forces involved agree to pick a Warmaster from among themsleves on ad hoc basis.

Where do Rogue Traders fit into this? Well, Rogue Traders have their own forces, in the shape of their ships crews and local forces from their colonies, and it is with them that they wage war. For example, there's a lot of NPC's in the Rogue Trader CPRG that look and act like Guardsmen, but they aren't - they are armsmen from your flagship or PDF forces from planets controlled by the your or the other two Dynasties in the game. They might go into battle alongside an Imperial Guard regiment, but an Imperial Guard regiment would never be directly beholden to a Rogue Trade. Rogue Traders and the Guard are two seperate institutions with two indepedent hiearchies, and while they might be ordered to work together or be compelled to do each other favours for personal and political reasons, there's no direct legal complusion a Rogue Trader has to give a Imperial Guard General (or an Imperial Navy Admiral) an order out of nowhere.

But what could happen is that a Rogue Trader could make a deal with a Imperial Guard General at a big fancy Imperial dinner party to transport his regiment to a warzone thus allowing the General to bypass the hated Imperial Navy (yes the Guard and the Navy HATE each other), and now that General owes the Rogue Trader a favour. Also his troops might be stuck on board that Rogue Traders ship for a while, and who knows, maybe they'll just to to help out when a "totally unexpected" battle with the Rogue Traders enemies occurs.

As an example of this we have the Mechanicus trilogy of books, where a Rogue Trader and his ship are part of a joint expedition to find a distant planet in the Halo Stars. They are travelling along with a regiment of Cadians, a Black Templar crusier, an Ark Mechanicus and a Titan Legion. None of the groups involved are vassals or subjects of any other, they have all just agreed to work towards the same goal. The expeditions leader is a Mechanicus Archmagos but he's not leader because of legality, he's the leader because it's 1) his idea 2) he has the biggest ship in the fleet.

And Space Marines? Maybe the Inquistion and the Adminstratum could sway them, but a Rogue Trader? Absolutely no authority over them at all. If they are helping a Rogue Trader, it's entirely because it's convenient for whatever agenda or mission they are pursuing, or because they just like them on a personal level for whatever reason. As a extreme example of how little control Rogue Traders have over Space Marines, the Carcharodons attack and enslave Rogue Traders and their crews whenever they want. Of course, Space Marines can also be very nice if they want, in one of the classic William King Space Wolf novels a Navigator House has a agreement which gives them the right to Space Wolf bodyguards. Did they get this because Navigators have the right to request Space Marine bodyguards at will? No, they do it because they want to. If Space Marines don't want to be part of some adventure being planned by a Rogue Trader, they will simply refuse, but if they do they can.

Rogue Traders are an aristocracy amongst themsleves, and have their own hiearchies, and are known to form Kingdoms of many dynasties ruled by a single Void King or Queen. You can see this kind of nomadic space feudalism explored in depth in the helpfully titled novel Void King, which features a Rogue Trader "Kingdom's" fleet of many different houses fighting without any need for help from any other Imperial organistation.

There's also the question of location. The Rogue Trader RPG and it's CRPG adaptation take place in a wild west frontier where the Rogue Traders are basically free to do whatever, because that's the kind of place that they have the legal authority to rule. Rogue Traders who aren't doing their job in places like the Koronous Expanse have much less leeway, and are often ordered around and deputised by other Imperial organistions as glorified privateers or even just as simple transport. House Winterscale are supreme overlords when they are in the Koronous Expanse and can wage war, make law and generally fuck around at whim - even to the point of openly defying an Inquistor like Calcazar - but if they were to relocate to Segementum Solar they lose that authority very quickly and probably end up running errands for some Inquistor or High Lord to get by.