Trying to make the best argument for those who are not disciples of The Shift... If there was some way to know that Browns have a unique ability to flood their system with catecholamines (I have no idea what those are), sort of like the old stories of kids on PCP being impossible to subdue, then maybe that would support something other than a 77gr TMK. Like a 140gr TMK.
Maybe.
Catecholamines are a group hormones colloquially referred to as adrenalin.
For a body shot to a brown bear that is already mad to crumple him, you are looking for a permanent wound channel that roughly includes the entire chest cavity. Even then, rather than this being instant incapacitation from destruction of heart/lungs/arteries it is likely the damage done to the skeletal system and spinal column that results in an instant stop. I.e. you are breaking the animal down.
Off the top of my head, a 375 Cheytach pushing a 350 gr TMK type projectile north of 3000 FPS might allow a body shot to work for reliable near instant incapacitation on a large brown. Someone should test it out.
Nerd alert:
Adrenalin is a brand name of a single hormone epinephrin, like Kleenex is a brand name of tissue.
The complex neurohormonal response we typically refer to as fight or flight is not nearly as clean as taught in text books. Catecholamines are one portion of this, with the release of hormones like epinephrin, norepinephrine, and dopamine, but even this misses the role of hormones like DDAVP and angiotensin II, making it an incomplete description as well. It also misses the neuro portion of the response, which involves both sympathetic and parasympathetic activation to prepare the body.
The sympathetic nervous system is traditionally described as being responsible for fight or flight. However, pure sympathetic activation would make urination and defecation impossible. Because the body wants to shunt blood away from the guts as well as the fact that empty hollow organs (bladder, intestines, stomach) or less likely to be damaged in a traumatic encounter, the parasympathetic nervous system is frequently hyperactivated in regards to these organs to forcefully empty them at the start of a stress response so the sympathetic system can then shut down their function for more important things.