It may be recent legislation, but banks must have an SS number to open a new account for a customer. I know because My four year old just opened her first acount last week when her piggy bank became full. The account officer at the bank revealed this new regulation to me when we went in to open my daughter's first account.
Yes, but the difference is, your daughter is a legal American. If she was an illegal alien, things would be entirely different. I don't mean to be snide, that is just the way it is.
One of the threads on the Matriculas Consulares has been pulled. I am still looking. Maybe another FReeper can help us out.
I'm proud of you and your daughter for opening an account. I bet she is really happy.