I might be insane, but a song played when I was listening to a neighborhood radio station. When I went to go look at my library later, the song showed up there. I don't own the song (or at least I didn't see it in my iTunes library under that name) and I don't think I've ever played it on my iPod or played it in iTunes or Windows Media Player from a friend's device. So I'm not sure why it would be there. Did I actually play it somewhere and have it scrobble or did listening to the song on the neighborhood radio add it to my library?
Listening to the song would have added it to your library. Think of your library as pretty much every song last.fm has counted as a "listen" or "scrobble".
How these scrobbles are counted depends on which client you use to listen to them with. For example, the last.fm desktop client has a setting that lets you decide how much of a song you need to listen to for it to count. I believe listening to a song on your iPod/iPhone will only count as a scrobble if the entire song was listened to (last time I checked this was because of restrictions in the iTunes API).
I just looked this up, too. I'm not concerned with owning or not owning a song. But songs are showing my in my library that I haven't' even listened to! My library should only consist of songs I put there!