My experience with joint bank accounts in the US is that they only take the Social Security number of one person, who is the primary account holder, and that person is responsible for all taxes. It was this way with my former joint account with my ex (I was the primary account holder, and only my SS number was on record) and the joint account I have now with the sister (she is the primary account holder, her SS number, and not mine, is on record.)
So I would guess that you will not need an ITIN for her, but you could call the bank and ask.