There is no question in my mind that holding a fish like that causes broken jaws. I have seen it a few times in my pond. A friend caught a four pound bass a few years ago and carried it by the jaw for about 100 yards or so to where I and my camera were. When he got there the jaw was broken and bleeding. I did not think the fish would survive and suggested it be cleaned. My friend insisted on releasing it. For the next couple of years I caught a fish with a mended broken jaw in about the same place as where my friend caught the four pounder. I think it might have been the same fish, but not sure, and each time I caught the fish it weighed less than before. i believe the broken jaw hindered the fishes ability to feed.
I was even holding a 14 incher by the jaw once and felt the jaw break. I had really put an angle on the way it was being held.
However what gets me even more is when anglers lay the fish down on the grass, the dock or the carpet in the boat. Professionsals do this all of the time. When you see the slime on the dock or carpet you know that you have removed some of it's protective slime.