Hey mate thanks for a genuine question :
ideally the brain gets blended if one has a 2nd hand/cheap blender, then mixed with some water and heated up but as you mentioned, not boiling at all! just warm.
what happens is the fat an oils inside the brain, so mostly oils (tanning agent) will mix in with the warm water an be one solution for when it is soaked into the hide..
The water can be cold but it may not penetrate as well an may end in a untanned hide, so to go to all the effort to get it ready to tan and to skimp out on a 5 minute heat up would be the Shortcut that drew you back to square one.
its just more user friendly to freeze as one unit in a tin/bag than gathering a bunch of mush off the grass lol..
ive done alot of Euros, know all about the rain coat of fluid that the brain turns into an the extreme speed it flys out of the spinal column

preferably a garden hose with the rate slowed down alot works fine. small band of sinue stuff will hold the brain intact unless it was boiled for a good period, which makes the extraction 'easier'.
With your Buddies end result, was it worked and ended up a softer hide or a harder 'floor rug' type? this all has to do with time spent on working the hide after the tan an prior to smoking.
ill have full hides done soon, about to get a heap of cow brains from the abbatoir, makes it less an issue with stagss skulls an probly be able to just skin the animal an take the meat as opposed to the skin meat and its head...
Cheers mate