The collar issue is not just with Yorkies, though they do have a predisposition for weak trachea. Small dogs in general do not have the muscle tissue to protect the cartilage of the throat area. Very sad that a trainer would reject all proven information concerning a Yorkie because she has never tried other methods.  
Anyone that needs a pinch collar to train a puppy is sadly lacking in proper training methods. They are usually reserved for very difficult training problems with large adult dogs.  Even a traditional choke collar should always be kept loose except for a slight jerking motion needed to get the dog's attention. Even larger dogs can become injured from improper use of a choke collar. 
Puppies in particular have no protection of the trachea area. 
Collapsed trachea is very often a degenerative problem in a Yokie. The trachea may start out seemingly fine but as time goes on deteriorates. Use of a collar only speeds up the process.     |