I believe that a vertical hold from the gill or mouth probably does not harm the fish......
BUT.....I DO Believe that a vertical hold from the tail {upside down} on a large fish can KILL it....Especially a Muskie or Large Pike...THE ONE AND ONLY Muskie that I have on My wall was killed that way...I was a rookie Muskie angler and didn't know. I actually "felt, heard" the vertebrae separating..kinda like cracking knuckles..
In no way did I intend to kill this fish , I was lifting it from the ground "caught from shore" to cradle it for a safe release..... I spent 30 minutes in the water with her to let her go ... but alas no go...can't swim with a broken back.
Although not that big at 49.5 " 30Lbs...she's a reminder on my wall.
Just my 5 cents.
RFS