Norm, I'm certainly not a Biologist but also can't credit birds with stocking ponds.
Fish eggs are too slick and slimy to stick to a birds feathers or feet. However, if they did, they would almost certainly dry out while being hauled through the air. Ok, lets say they got to the new pond in some sort of viable condition. Most game fish eggs are necessarily fanned and thus aerated by a parent. The parent also keeps them from becoming covered by silt. The only exception I know of are eggs that are laid in running water. We don't have any of that in a pond. Next, the parent usually guards the young fry from opportunistic predators. We ain't got that either. If they survive early predation, they have to worry about all kinds of predators. I once read that a 5 lb. largemouth has beaten over 10,000 to 1 odds.
On the other hand, I once told Bob Lusk that I would like to get some mosquito fish. He said don't bother buying them. I would probably get them anyway. How? He said he didn't know. Hey, maybe the stork does bring babies.
