I have never found the above quotes to be accurate concerning leaving the skin on. When I was growing up, all the old timers, weather permitting, hung their deer with the skin on for several days to a week or more. When I say old-timers, I am talking about men who came of age from about WW1 to around WW2. The deer were almost always hung outside in a tree. Didn’t matter much if the days were a little warmer as long as the nights were cooler. This was done to age the meat. We ate a lot of deer meat and I can’t ever remember getting a spoiled piece or anyone having a deer go bad. If fact, if memory serves me, the meat tasted better, being more tender, than the quickly processed meat of today.
My view on the whole thing is that the old-timers lived a lot closer to the land than we do today. They hunted for food, not for horns, and couldn’t afford to let meat go to waste. Everything they did was for a practical reason, for a specific purpose, based on experience, not because they read it in a magazine.
I am not saying getting the hide off and cooling the meat quickly is a bad thing. I am saying there is a lot of bad data out there about meat spoilage due to leaving the hide on, or having to get the meat cooled immediately. Personally, based on actual experience, and I am talking truckloads of deer over multiple decades. Leaving the deer hang for a week with the hide on is certainly not going to hurt the meat, and will likely improve texture and taste.