The words "tight" and "firm" are relative in that different people will use them differently in terms of pulling the gun into your shoulder. As a kid I read lots of Elmer Keith articles and a couple of his books. He advocated pulling the gun firmly into the shoulder pocket as holding it more loose gives the recoiling gun kind of a running go at your shoulder. So when I grew older and started shooting big bore rifles and shotguns I followed his advice and still do when shooting clays and in the dove fields, time permitting. I don't call what I do "tight", I consider it firm. Like a previous poster, I hold the forearm in a positive manner but not tightly.
As a skinny 14-year old I had a friend who's Dad didn't own any guns, but decided out of the blue that he wanted to go deer hunting. Not knowing anything about guns he bought a .338 Winchester Magnum rifle, overkill for his intended purpose. Since they knew I liked to shoot they asked me to sight it in for him as he didn't know how. So off we went to the shooting range where my own Dad had a membership. I got it sighted in, after a fashion, although it took a full box of ammo. It was a thumper for skinny little me who hadn't hit his growth spurt yet, but because I pulled it in firmly it didn't beat me up badly. When it was the turn of my friend's Dad's to shoot he only fired three rounds. I'm sure he was holding it pretty loose. Said it kicked like a mule. I never knew if he went hunting with it or not.
Anyway, pulling the gun in firm works for me as a sore shoulder has never been much of a problem. As in much in shooting and life itself, there isn't always an absolute right way to do something, there is just your own personal way to do it.