The solution above didn't work for me. However, using Get Info on the song in question, I noticed that the account information was correct, but there was no "Purchased By:" entry. This was pretty strange, given that I'd purchased the entire album, and all the other songs had this entry.
Anyway, long story short, on a whim I tried deleting the song (to Trash) and downloading it again from iCloud - the newly-downloaded file had the Purchased By line and played fine.
Odd, but there you have it.