The GSC cannot force the TSA to allow someone airside, IIRC, and the TSA cannot technically deny someone from flying (though by delaying them until they miss the flight, the TSA effectively does hold that power).

From what I understand, the bit about the GSC not being able to "overrule" the TSA only means they can't force the TSA to let someone through the checkpoint with unresolved security issues. I.e. if your bag alarms and you don't want to allow a hand search of it, the GSC isn't going to be able to force the TSA to let you through. However, in cases where the TSA starts pulling the, "Do you want to fly today?" routine, the GSC (and LEOs, sometimes) are able to help resolve things satisfactorily.