The discussion is really not whether it is possible or even whether it occurs rarely, but really about far more likely causes of unwanted stocking of ponds. Why start with an unlikely explanation when far more likely and substantiated causes are known. It is almost certain that bird-caused stocking very rarely occurs, just like water spout tornado stocking. Whether from eggs or multiple fish is not really the focus. Its possible and has almost certainly occurred. The real question is whether it is so rare as not to be likely in any specific case.