I agree that it could happen and probably has. But the odds are truly astronomical regarding any given event. Somebody wins the lottery but that requires human intervention.
I don't believe that a bird has ever consciously stocked fish.
The odds of eggs sticking to feet, feathers or fur are also pretty skinny. The odds of such eggs remaining viable after flight increase the odds. Lets say that the first 2 events did happen somewhere in neverland. Now, lets assume that somehow the wad of eggs came off the donors feet, fur or feathers into a pond. We also have to assume that those eggs had been fertilized by a male. To get the sunlight that they need, it would have to be in shallow water. We would also have to assume that there was enough wind/gentle waves to aerate them without them becoming covered with detritus. Lets further assume that it was a pond with no other fish of that species. Now, we need to assume that no bugs ate the eggs. That also means a BOW barren of anything like other small fish that would/could eat the eggs or any fry that somehow hatched. That means that the ever present opportunistic minnows/YOY just overlooked the easy meal. I may have even missed a couple of steps here.
So, we start with astronomical odds that keep getting hugely skinnier at each stage. The odds are probably worse than me winning the Powerball lottery. BTW, I don't play that sucker game.
By now, I'm betting that some scientist has probably tried to duplicate the process but failed. Anybody ever heard of such an experiment?
I'm not a scientist but I tried it about 10 or so years ago. I bought a white duck at a flea market and sacrificed it. At that time, BG were nesting and I ran a male off a nest. I tried to get the feet and feathers to stick but it didn't happen. I realize that it was just one time by a non scientist so that is no proof that it couldn't be done in a lab under controlled circumstances. But a pond isn't a lab.
I'll take the odds on Mudcat Joe.