I've cooked Lake trout that way before
Gutted and wrapped in foil with seasonings.
Built a fire, let it burn down to bed of coals and placed a flat rock in center to hold the fish.
The fish came out excellent, a little more time consuming that placing foil wrapped fish on a grate over fire but probably less chances of burning baking it on the stone.
Another use for hot rocks is to warm your sleeping bag in cold weather.
One late SEPT trip I brought a leather pouch I made out of heavy scrap leather. Heat a nice flat rock in campfire and put in pouch.Make sure flap of pouch is long enough to fold over and wrap completely around rock. At bed time put in foot of sleeping bag and you'll stay nice and toasty for hours

That's the first thing I thought about when I read about making the leather pouch for the hot rock
The article mentioned that scene and that's why the flap on the pouch wraps completely around assuring there are no incidents like in the movie
Setting your sleeping bag/tent on fire and maybe yourself wouldn't be something you'd want your friends to hear about

I think it was a few years ago I went up to The Fort at Grand Portage for the festival activities, and that is where I noticed cooking the fish on a slab of rock.
I also noticed the boiling water as you mentioned but they didnt use a bag they had a bowl made of birch bark.
If a birch bark bowl was filled with water/soup and suspended over the hot coals, Id think it would catch on fire. Guess it depends on how close it is.
They had alot of games they played there also. The returning champion of several years was back to defend his title on how far he could throw a heavy rock. He won again.
They had relay races, of which part of the race involved a paddle, and a shot of brandy and balancing. Well you get the idea. Fun times at the Grand Portage!

Regarding the sauna, use two long sticks to act as tongs or holders of the hot rocks as they come out ot the fire.  No one gets burned.  About thirteen years ago I came across a makeshift sauna built on a great island on Kawnipi.  The framework of the sauna reminded me of my Eureka Wind River tent.  All you had to do was tarp it and there was a small depression for the rocks.  This was fifteen feet from the waters edge so a cool dip was near by.  This island also had the most ingenius crapper.  Two lengths of pine trees about 7' long were twined about two and a half feet off of the ground between two other trees.  All the bark was burnished off and the seat area had duct tape, so no splinters.  Along with the great fire pit this was a great star site.  But I digress .