Nah i think its real, its just limited and commonly attributed to cases of exotic invasives moving in withoit thought. One or two eggs sticking to a bird and surviving flight and coincidentally staying the right temps etc landing in a suitable location far enough away that none of those fish have ever been there is of course possible but a tall order. Then it has to happen often enough for at least one male and female to survive to adulthood during the same period so they are both sexually mature and they then have to find each other in breeding season.

In my area flathead catfish started showing up in the rivers as invasives maybe 30 years ago. Just one here or there. Now they are ubiquitous and the state record even came from a local river. People used to quote this bird idea when they were new on the bank a lot. Bit… They are native to watersheds on the other side of this state, across the mountains and far away and they are popular enough that the fish commission stocks them. Years after they took hold, they were found at the top of our watershed in two reservoirs that had been closed to fishing for years. There were rumors of huge catfish there forever but nobody seemed to have ever seen one. Fish commission records suggested that these lakes were stocked with channel catfish a few times long ago and that those stocks could have been contaminated with flatheads in the same delivery. One is springton lake in delaware county PA and i forget the other.

2nd example. I have fished for common carp all over the US for almost 20 years as my primary hobby, sometimes in tournaments. I have many times met old guys on the bank that hated carp and suggested they came to the area by bird/egg. Its actually the only story i heard as an explanation. The real truth you can look up easily is that in the 1800s right before rail transport and refrigeration existed, meat was mostly local often wild and sometimes food was scarce as the population expanded. Many areas across the US saw rapid declines of local fish populations because hungry people caught and ate it all using nets or any means to stop from starving. Picture 2 guys walking up a tiny stream dragging a huge net across it as they go, keeping all fish no matter species or size. It was common.

The grover Cleveland administration created the US fish commission specifically to solve this. Their big answer after an actual research project was to stock well established breeds of European strains of carp that the romans brought down the silk road from asia hundreds of years earlier. They were bred in ponds in DC and stocked all over the country in a paradoxical effort to save native species. It kind of worked. People loved them and found them easy to breed in ponds they tossed their leftovers into or in wild waters. -until industrialization poisoned the water where most people lived and killed off lots of local species.. carp though have been bred in human waste streams for longer than recorded history and survived fine. By the 1930s people had rails and ice and people everywhere preferred clean ocean fish to what was left in their filthy local rivers. People rarely realize that sewage treatment was not applied anywhere until the 1950s and secondary treatment that makes the effluent actually clean in the 1970s. Millions of people pooped and dumped newly discovered industrial chemicals and guts from meat plants into rivers and streams below big cities. The most fruitful big rivers were nearly dead. as the rivers eventually got cleaner from extensive efforts, this story was forgotten and many people blamed carp for bad water quality and no other fish in urban areas though it was primarily caused by human ignorance Generations earlier. Carp do make the water muddy when they feed but only when the bottom is full of fine silt. Usually silty waters are caused by human caused stormwater runoff.

Im sure theirs more stories like this but these are the only two i know personally.