I bought and downloaded a song in iTunes on a PC of mine. I never synced it to my iPhone. Well, I got a new computer, and no long have the old one. I think there might be a problem now.
Here is what happens when I click Check For Available Downloads in iTunes:

And here is what happens when I click on buy, for the song in the iTunes Store:

Is this a case of a badly worded dialog? I've seen something like this before in the App Store when I needed to reinstall a paid app. In that case I "bought" the app again, the second time without being charged.