I just don't understand this at all. The reverse, maybe I get. You want your GC involved because calling and enforcing targeting rules should be a help in defending against claims arising from head injuries (CTE) and refute the whole "the league doesn't care about it's players". I maybe I would understand if the GC is in that loop, but in that case he or she would be overruling the officials and saying "you guys got this wrong, that is exactly the sort of blow our rules are supposed to be addressing, because they are unreasonably dangerous, blah, blah, blah".
Overruling it the other way? Well, I have some theories about that, but none of them are good nor do they contribute to a positive image for that league or individual.