Yes, you're probably right. I was kind of hoping someone else might have experienced something similar. I have narrowed this down to the Registered Users group specifically, so at least I know it isn't something funny with one of our other groups.
When I re-add "user" 0 to Registered Users, things work again. So something somewhere in our installation needs at least read permission for Registered Users. I just have to figure out what that is, and also figure out why it is different between our main and dev servers.