Didn't realize that. Maybe I was confusing it with their service acting a registry (as opposed to registrar): https://www.google.com/registry/index.html

I could have sworn it was possible to register domains directly through Google, but I guess it could have been a cleverly disguised front-end to another registrar.

I don't know about that. I registered one through Blogger, went to renew it later and they were no longer offering that service from Google.