Here is the Missouri Conservationist Magazines take on the subject...
Q: I heard that birds can eat fertilized fish eggs from one pond and then, through their droppings, �seed� another pond with those eggs. Is that true?
A: The digestive process and the anaerobic conditions that the fish eggs would experience in the bird�s gut would be fatal. It may be possible for fish eggs to be moved by birds if the eggs were stuck to their feet or, more likely, contained in vegetation transported by a bird. A lot of things would have to go right for that to occur and it would certainly be very uncommon. When fish appear in an unstocked pond, it is usually the result of wild fish moving upstream or downstream from other ponds or streams in the watershed during wet periods or due to intentional stockings.
This came from this site...
https://mdc.mo.gov/conmag/2011/09/miscellanyI don't believe this is something that happens on a regular basis, but it happens.
I remember reading a thread (probably on PB) that suggested that the large herons will regurgitate their last meal (or their meal in process of going down their throat) if they get spooked. I though it sounded fishy, but within a week, oddly enough, I spooked one in the creek by accident and I saw something come from its mouth. It was a minnow of some sort and was still alive.
I suspect that almost any egg from a water animal could get transferred to another BOW on occasion. I would tend to believe the above quote in saying that plants being moved around by land animals are more likely to carry the eggs.