I should add that even if the use of someone else's tune was inadvertent, royalties may be due to whoever first registered a copyright for that tune.

I believe this was the case with George Harrison's use of the tune to "He's So Fine" for his song "My Sweet Lord."   I didn't notice the similarity of the (pretty much identical) melodies until someone brought it to my attention when Harrison was sued for plagiarism, and I'm inclined to think he didn't either. But I think he had to pay some pretty big bucks in royalties, anyway.