Pinch collar on a puppy?
Okay, first of all, proper prong collars don't hurt (put a Herm Sprenger on your thigh or arm and yank it - you'll see what I mean).
Slip collars, choke collars and anything that chokes the dog can really cause tracheal/esophageal damage. Of course, any collar used improperly can cause damage to the dog.
But for a trainer to immediately go to the prong is really silly, IMHO. Of course, there are staunch supporters of "this and that" type of training that will hold on to their concepts to the bitter end as gospel.
I think that a puppy needs to be exercised in a lot of fun, then enticed to learn his commands with positive reward. Negative feedback is reserved for when a young dog knows his commands for certain and is rebelling.
That being said, prong collars (the right ones) are actually better than some others.
Myah started on a regular, soft puppy collar, graduated to a soft martingale (3 mo), then a chain martingale (4 mo). But at 5 mo, she's so mellow and easy (that's her temperament, so I'm lucky), that she does fine with the soft martingale.
I did buy a Herm Sprenger prong collar for use when my elderly mom walks her. Doesn't hurt her AT ALL, and gives the kind of pressure that makes her listen to my mom so she doesn't pull her (my mom has arthritis, so corrections when pulling are hard for her).
Are you sure you want to use this trainer? There are always good things to take away from trainers and their sessions. Eat the hay and spit out the sticks, as my grandfather would say.
If the trainer doesn't allow you to modify anything, then I would say that's your cue...