I think we are conflating a few concepts here. "Offhand" as it applies to hunting, to me means, shooting unsupported in a generally standing position with a sling wrapped if possible. I think some of the posts are adding field expedient rests and some combination of sitting with elbows on knees with a sling (I call it chair prone as it is nearly as accurate as full sling NRA prone for me).
Following are the dimensions of the NRA SR-1 (100 yard) high power target. I shoot a lot of high power with a lot of very good shooters so it makes a good yardstick for me.
4.2 100 Yard Targets (a) NRA No. SR-1 Reduction of the SR Target for use at 100 yards to simulate the 200-yard stages of the National Match Course. Aiming Black (inches) Rings in White (inches) X ring ..................1.35 10 ring ..................................3.35 9 ring ....................................6.35 8 ring..................................9.35. I've omitted diameters larger than 8 ring as I think they fall outside of useful field accuracy.
In high power matches, I have only ever seen one clean 100 score fired with something resembling a hunting rifle (CMP service rifle 4x optic). I've seen more with match rifles, but if you look up what a match rifle is, you'll see they bear little resemblance to what you'd hunt deer with. These are generally on the 200 yard target so there is a bit more range involved, but the targets are the same in terms of MOA. It is fairly common with the top shooters to see a 10 round string all 9s or better, falling into what I think the consensus is for acceptable field accuracy. It is also quite common to see a top shooter string together 7 or 8 10s and a couple of 8s or a pulled shot into the outer rings. Looking at the dimensions of an 8 ring hit, we are getting into the realm of possible wounded deer from a guy who probably won the match against a tough field if he didn't choke a prone or sitting stage. We are talking about people who play this game at known distance and relatively stable range conditions who fire hundreds, sometimes thousands of rounds in said game and practice for same per year.
I think it would be the rare hunter who could take his or her hunting rifle out and run a string of 9/10 shots 9 or better offhand consistently. I can't. I might do it half the time, but the other half, odds are I'm throwing one too many 8s or a "bad one" into the mix. Now you add some extra support...either a field expedient rest, or some extra body mechanics in tandem with a tight sling wrap, and the odds improve considerably. I consider myself a 200 yard chair prone, sitting, kneeling, prone or field expedient rest shooter on game. Add in a solid rail with padding and a good shooting position and I'll push it to 400. Practice on 6" diameter targets bear this out. Offhand/sling, I'm confident at 75 if I feel the shot. Not to say I haven't shot farther offhand, and done it successfully, but I was knowingly pushing my luck.