I've had the same experience (although I don't remember if it was specifically the melody being claimed). I don't always bother to dispute them (in my understanding, most of them just claim ad revenue, and we don't run ads), but sometimes it annoys me enough that I do. (The organist and people singing are pretty clearly pictured, and I get especially annoyed when it's a capella.)
Historically Google only put ads when requested by the channel, which required a fairly significant threshold of views and subscribers and supposedly manual review by Google. Some time last year they started a switch towards serving ads on all videos, regardless of the preferences of the channel (whether you’re big or small, whether you want ads or not), which I hear has been progressing steadily further and further. (I wouldn’t know. The internet’s too dangerous to view without an ad blocker. I also just generally hate ads and only see any at all when I leave my peaceful rural environs and go to the big city.)
My reading of the situation at the time was that if there was a copyright claim, the video would be monetised in certain regions (depending on the claimant). So once I cottoned on to the situation, I always disputed the claims before publishing, so that no one would be fed ads. Now, who knows. Once I returned from India to Australia I stopped uploading the videos personally, and I don’t intend to publish any of my own stuff that I might make to YouTube.
