I don't think I'm being precious at all, Steve. I write songs myself as do a number of my friends, and may well use parts of, or whole tunes, that are trad or out of copyright: this works well especially for humorous songs. In fact, as I'm not likely to record such songs or play them to a paying public, I might well use copyrighted tunes as do several friends as well. (I'm a session person, not famous - maybe infamous!) But for a more serious song, I do like to use my own tunes where possible. I'd really rather not be accused of plagiarism for my own songs, and as I said, it is possible to modify tunes so that they no longer resemble other known ones.
As for my friend, it was just that the song to which I was referring was such an iconic song, well-known to many, but obviously not to my friend, that I thought it best to tip him off privately. He did agree that "his" tune was almost identical and thanked me for telling him: no offence or umbrage taken by him.