Summary:
This was reported as a security vulnerability, moved to a Gmail bug report, then closed with the status "Won't Fix (Intended Behavior)". [0]
Anyone can DoS any gmail inbox by exceeding the incoming email limit. Gmail just starts rejecting emails to the target account. They have known about it for years, but don't seem to care.
Edit: The most frustrating part is that I have stopped receiving email for 6 days now. I was told second hand that an employee at google was also affected and the spam team was going to deploy a fix. There was about a 12 hour window yesterday when the email started arriving again. It is frustrating that their bug tracker contradicts what is actually going on inside their organization.
There is nothing in the UI that indicates it is hidden. They said it was a known issue and they won't fix it, so it doesn't make much sense to keep it hidden.