I did get a response from Google. Here's what they told me:
I know this can be confusing, so I hope this explanation will help clarify.
It appears that you do not actually have a full YouTube account. If you see your email address or Google+ name in the top right corner, it's just informing you that you're logged into your Google Account.
Without a full YouTube account, you have no public presence on YouTube. In order to do things like leave comments, upload videos, and make playlists, you’ll need to create a YouTube channel. To create a channel, please visit this page: http://www.youtube.com/create_channel
So a Google account means you have a YouTube account (really, it's the same account -- so you can't delete just the YouTube part), but does not mean you have a YouTube channel. Confusing because you can still "like" a video and do some other things without the channel.