Somewhere it needs to be in writing, or at anytime the author could lie and claim they never gave you permission. And technically, all music is copyrighted the moment it is written, even if not registered.
Odds are, if he said you're ok, you won't have any issues, since he will most likely never put in a claim. However, there have been many legal problems that could've been prevented if there was something in writing, even if it was a saved e-mail.