When I opened the animal door, all of the baby ducks immediately ran out the door, jumped into the river, swam to the other side and started eating Grass there, thereby invalidating my test.
I put in fences with gates, so they had to go into the water in order to go anywhere other than those two tiles of land. Later on, I found out that the tile in front of the animal door was mandatory - while Ducks will swim in the water, they won't jump directly from a Coop into the water. I left one land tile in from of the door for humans, so I could get in and out, and one in front of the animal door. I didn't want to use a Deluxe Coop, because the auto-feeder would make it difficult for me to tell how much hay the Ducks were eating. On the Hilltop Farm, I built a Big Coop near the north bank of the river.
Of course, the guy who programmed this game had some very weird ideas, so it was possible, but I decided to put it to the test. I suspected that it was actually the fact that there were rivers going through those farms that was the key factor, and the fact that the Hill-top farm wasn't included was due to an oversight. It didn't strike me as plausible that the Riverland and Beach farms would be treated as special cases, even though those are the only two mentioned in the Wiki.