Why does a high school kid have a credit card? Without that unique identifier, they can't datamine.
But really, why not have a credit card? If she's not building debt, I don't see a problem with having one.
Minors can legally enter into contracts. Those contracts are entirely binding on the non-minor party. The minor is the one that can repudiate the contract before the age of majority to void it, but otherwise, it's a perfectly valid contract. If the minor remains bound past the age of majority, the contract can no longer be voided, either.
There are credit cards marketed directly to teens.
More common than you think. On the other hand, I was living on my own at the time.