You are correct and that is why it wasn't a first down and was not challenged:
If a runner (including a quarterback) gives himself up, then he is down where the first body part touches the ground. The runner should not benefit from additional yardage after the first body part touches. Defenders do not have to go down to initiate contact to stop a runner from gaining more yards after he contacts the ground.
A quarterback does not have to slide feet first to be considered to be giving himself up. Regardless whether the slide is feet first or head first, as long as he gives himself up, he should receive the protections afforded to him as a player in a defenseless posture.