I don’t have the time to find the research. I can only report what I found and you can choose whether or not to believe it.
As for your reasoning, most birds do not have a phallus like a duck. They simply put their cloaca next to each other. Maybe that is how? Also, duck phallus shrink to...
Yes, they have. When I first heard this I thought the same as you. My degree is in Biology so I searched Scientific articles to see what they said about it. Sure enough, documented cases. Of course I did not find them now with a quick search but here is a bbc article explaining it...