The problem is that I, as a normal editor, have no way of verifying anything when User:Joe_Blog changes something in an article and just cites "Personal Correspondence". Do I leave it there or not?
I say not.
It depends on the kind of information involved. If it's routine personal information, it should probably stay.
It also depends on User:Joe_Blog being an entity that allows verification of its personal correspondance. Anyway we seemed to be agreed (I think?) that correspondance to the Wikipedia Foundation (name?) can be cited, so anyone finding incorrect bio information on themselves has a fairly easy way out - email them and cite it. If they don't believe you're you, then you may have some more hoops to jump through.
Steve