Interesting question. I've found that, after I have been playing a song for a while, I tend to change it, sometimes substantially in both lyrics and melody. I think that's a pretty common trait amongst us all. It's sometimes called "the folk process". I think of it as analogous to Icelandic "land-taking". It's making the song mine, whether I wrote it or not (usually my own songs undergo this sort of sea-change over time as well), as well as keeping it interesting. If this doesn't happen, it's usually a pretty good sign that the song is not for me and I abandon it.

I have to "live" with a song for a while before I feel comfortable with it, I've found. Then the arrangement becomes "mine". Legally, it's probably another matter, but I don't worry about that too much (unless I'm going to record it).