[nitetrane98]

Presumably, the trainer must have said something to the effect, "Use whatever kind of collar you want, I recommend a prong collar." I don't have experience with the Martingale's. Used properly, a prong collar can be a very effective tool. Just because the prongs are there doesn't mean you have to bury them a half inch into his neck. The leash issue thing might just be a manifestation of general hardheadedness. A leash, of any kind, represents restraint to a young knothead pup. Obedience training is for the purpose of him obeying you, whether he really wants to or not.
I'd talk to the trainer about your concerns. Ideally, we could train our dogs with a piece of yarn around their necks and I suppose there is something to be said for escalation of force, ie trying the least restrictive methods first. I'm sure the trainer has his reasons. See what he/she has to say.