Why'd you need to see her driver's liscense? If it was in regards to a credit card transaction, that's a violation of the merchant's agreement with the credit card company.
We need a government-issued picture ID* in order to start an account, and we need either a card or ID. You can buy all you want without an account, but we need proof of identity if you want to rent anything.
I know a lot of people absolutely
hate this, but it's really not that unreasonable. The store I work at is really small, and we still have about 20,000 accounts and get hundreds of people each day. There's simply no better alternative. The information recorded from your ID is no more than what you could find in a phone book.
Basically what I'm getting at is that being a customer doesn't mean you don't have rules to follow when you enter a store.
*read: driver's license. It's the absolute bare minimum. Some locations need way more proof of ID.