I've never heard of someone without your social security number having the ability to do anything to your credit.
It was an error on their part so take that as you will, but... scary letter != inability to borrow money.
(And just for the record, I no longer subscribe to that rag.)
A rather famous example of this is when Columbia House sold off accounts from their scammy operation to a debt collection agency, with many folks unaware that the company claimed they owed money.