So I did.
I thought.
I restarted iTunes and quit it again.
You know... just to be sure.
Xcode just looked at me like I was stupid.
So I restarted iTunes and Force Quitted it.
Ha!
(That was not a Star Wars reference.)
Xcode was laughing at me then.
So I started Activity Monitor. It's in the Applications/Utilities folder. Or you can type "Activity Monitor" into Spotlight which is what I usually do.
AHA! There is an iTunesHelper process. I quite that and a split-second later, Xcode finished its business.
Just a cautionary tale in case some of you have the same problem and hit The Googles looking for answers.