Gromit, I was assuming that photo ID was wanted. There's not so much of that about - I have my own passport (this family did not keep theirs at home), an old union card with photo, which few have, and a driving licence, but many don't have the plastic version of that either. If non-photo ID was wanted, the bank card ought to have been enough, coupled with the fact that the woman was a previous customer.
It may be some vital fact has been left out of the story. It all sounds rather odd.