We catch a lot of toothy fish up here in northern MN (walleye, northern pike, muskie) and I have never seen a fish injured by grabbing the gill plate. Of course, if you just jam your fingers underneath and tear up the gill tissue, the fish is going to die. As has been said, supporting the fish's weight under the belly with the other hand is preferred, but sometimes that isn't possible.
It's darn hard to boat a 42" muskie without a net, but it can be and is done on a regular basis.
Gill plate, fine. Gills, not good. Hand in muskie or northern mouth, even worse!