I was always told by fs people and guides, no guided trips were allow on the MMWT. So, what NP people say makes sense to me to a point. The principle is entry point. Usually the jurisdiction you enter rules apply for the trip...trips starting in the parks do not require a exit permit. I am not familiar with the commercial rules but based on what you have been told it appears to be some co-operation between the Park and Forest Services.

I would ask for a copy of the forest or park order that covers this type of thing...just to have my bases covered.

Also, you can exit via a Horseshoe Meadow Trailhead but that would make the trip one to three days more...figuring you would not exit the day you summit.