BUT as if by magic, if you log in within these 14 days, everything will be restored as if nothing happened, and they'll forgive you.
I can't figure out if this is a really bad case of eventual consistency or just a cooling off period they hope to entice you back with.
Last night a friend mentioned that she was able to remove her birth date last year but when I tried this morning there was no option on the web app. I emailed support@facebook.com, admin@facebook.com, etc. this morning asking for it to be removed and pointed out that this might be a huge legal exposure to them.
I'll add a comment to this comment if I ever hear back from them.