For the record, about this weblogs being deleted thing. As of right now, I have no idea how it is happening. Nothing is appearing in the Movable Type logs. Nothing is in the web server logs indicating a "delete this weblog" URL was hit. I'm going to increase the logging level of the database and see if I can't track it down via that. (Of course, to be able to track this down, it would need to strike at another unsuspecting user, which is unfortunate.)
In the meantime, I have removed the self-service delete-my-weblog option from the administrative panel. And, I have removed all of the code in the Movable Type base that performs a weblog delete operation. Though, I don't know how effective those measures will be to curb the problem.
Like the Blog@Case news items said, email the Case Blog Administrators if this happens to you. It takes a bit of time to restore a single weblog, though, because the backups we take of the database are full backups – meant to be used in the event of a database/hardware disaster to do a full restore of the system. To do these selective restores, one needs to perform a pseudo-restore of the whole system into a temporary location, meticulously pick through the resultant files for the necessary components of the blog you want to restore, perform a test restore of the blog in a test database, and, finally, actually restore it. It's a time consuming operation.