I got into a couple herds this year between 11 and 11.4k...treeline on the mountain varies from 11.2 up to about 12k on the mountain I was on... The one I shot was lower and on a different mountain.
I believe he stated he hunted up even higher. I understand that yes on occasion there will be game above the tree line but this clown made it sound like he was so tough that he could hunt higher than anyone else.
As far as the original question of would/could I do it? Sheep or Goat? No. I just don't have any desire to hunt them, just isn't appealing. They're kind of like Mule deer to me. There are two really good draw only units near me but I've never put in for them. For whatever reason shooting a Mule deer is about as appealing to me as taking back my ex-wife. They taste like s**t anyway (my opinion, no arguments please) unless you shoot them out of a farming area. Moose or Caribou, heck yes! I'd love to do a Canadian backcountry hunt for them. Somebody mentioned Bison...also something I'd love to hunt, but that one I'd be packing my black powder rifle. Best way to relate to a Mountain Man, without the horrible wading in frozen streams to reset beaver traps in nothing but buckskin skivvies. Those guys were the definition of tough! Grizzly? Solid NO. Bad enough to have to worry about them if Moose or Caribou hunting. A friend and his wife went on a Caribou hunt. He brought his .44 to wear "just in case". He told me that they luckily only saw two and they were a long ways out, but they resemble a Volkswagon walking around on the Tundra. He said his .44 might as well have been a bb gun after seeing how big they really are. Africa? Just to get to see it! Certainly wouldn't mind hunting something like Kudu while there. Zebra, elephant, Lion, no. Zero appeal.
Going back to the original question, I have no desire to hunt Mountain Goat. The idea of killing something in those mountains and having fall thousands of feet and go to complete waste is not appealing to be. I would hunt the Sheep species if it wasn't so expensive and hard to draw a tag. I hope to do Dall Sheep in Alaska some time. But, it would be a one time thing since it is so expensive. I have hunted elk, white tails and mule deer successfully, moose unsuccessfully. I was going to hunt antelope this year until COVID.