Of the composition of “Nightswimming,” in the interview “Automatic Track by Track” for Radio X, R.E.M. - Automatic For The People Track-by-Track | X-Posure | Radio X - YouTube, Mills said,
““Apparently, Peter wrote in some liner notes [for In Time] that it was a competition to see who could write songs for those lyrics, and I don’t remember it being that way at all, it was just something I was messing around with, because it’s really fun to play, and I would just sit down and the piano and goof around with it, and Michael heard it and said, ‘Keep playing that,’ so I did, and he started coming up with really beautiful stuff for it, and before long it was a song.”
As with the story of all the words for “Man on the Moon” being written at the last possible second, or of “Country Feedback” being written and recorded in one take, Buck’s oft-repeated story of the songwriting contest to set Stipe’s poem/lyrics for “Nightswimming” to music likely isn’t true. At the very least, his story and Mills’s story can’t both be true. As you note, people’s memories are not perfect, especially when they’ve lived lives as full of incident as the members of R.E.M. have. But there’s also pretty clearly a pattern of stretching the truth and gilding the lily, exacerbated by getting away with doing so for decades, as gullible journalists simply print whatever tall tales they are fed.
Mills has pretty consistently refuted some of the stories told by Peter and Michael, as when he fairly recently denied Stipe’s claim, from the Rolling Stone cover story on Monster, if I recall correctly, that the band briefly broke up during the final sessions for that album.