I'm just curious, particularly since the receipt from a T-Mobile store looks like a contract that you must sign. I remember this because I had to get a new SIM card from T-Mobile yesterday -- this was for a free data plan (T-Mobile's tablet 200MB for life plan, the plan is no longer available but I am grandfathered) and I had to sign a form that looked like a contract. Essentially, it is the mobile terms of service and that I won't use my tablet for any illegal/unethical use and, if I do, that T-Mobile can cancel my service.
I suspect that she bought a prepaid cell phone (paid full price) and prepaid service, and the "contract" is merely the receipt as I describe above.
If I'm wrong, and she signed a contract, I don't see how the employee didn't mess up. For postpaid service it requires a credit check, period; and T-Mobile's policies (from what I can find) is that they will not sell postpaid to anyone under 18 years of age. In that case, either your daughter is friends with the employee or convinced the employee to do something against T-Mobile policy -- in which case you go to the store manage, or to his boss, until you find someone willing to handle the issue in the store.