When this person is trying to "correct" you, I would simply call over your teacher to get your teacher's opinion on how it should be done. This would be a simple and direct way to allow your teacher to become involved in this situation so that it must be dealt with by the person who is responsible for the dojo.
Marc, I see one small fallacy to your suggestion. You have not allowed for the possibility that the teacher has already noticed the situation, and has chosen to deal with it by not dealing with it. To bring him in to arbitrate on the mat could put the teacher in an uncomfortable position or even to have to settle the matter in a manner that was not his preferred one. I think it would be better to discuss the matter privately with the teacher first, before putting him "on the spot".