As for fish colonizing the pond surrounded by an embankment, alot of people have told me that waterfowl can carry fish eggs on their legs. Not sure how true it is. I do however know sunfish and bullhead have a habit of appearing in new ponds mysteriously.
Then again sunfish and bullheads are commonly moved and stocked by anglers too, especially kids who bring fish home do not want to clean them, and dump them in nearbye waters. (when I was a stupid little kid and clueless of the consequences I was guilty of this and stocked a few small fire ponds).
Sunfish and bullhead eggs are both unlikely to be moved by birds as they are nest spawners on the bottom which is well away from where they might get attached to ducks. I'm yet to see any evidence that says anything fishy has ever been found on a bird. Indeed, most stuff carried by birds is very small, mostly plant seeds and some plankton species from memory. For birds to work fish would probably need to spawn directly onto the bird and have quite adhesive eggs. Then when the bird lands the eggs would need to detach onto a suitable substrate, hatch, both males and females survive, and then breed. It is theoretically possible, but seems extremely unlikely to me.
I think that people often underestimate other people moving fish around too. Even if it is done as a prank by friends, I'm sure it happens a lot more than people realize too.