Unless they are hiding something, no reputable dealer is going to deny permission to have a used vehicle professionally inspected. I can see where they might have a problem with where you are having the inspection done. In the past they may have had problems with a competitive dealer purposely giving bad inspections (yes, this sort of thing DOES happen), so there is that possibility. Ask them point blank. You really shouldn't have to tell them where you are taking it, but, the dealer does have the right to reject an inspector that they have had past problems with, after all, it is their truck.
If it were me, I would just move on.