First off, I agree that even the 22 LR or mag will do the job, but may not either be legal nor ethical. So no, not any choice above a 22 Mag will do.

Second. "Stopping power" is not Redneck BS. What would you rather have with you if you were say fishing along your favorite salmon river and a brown or griz approached and decided that you looked better than those fish he had been eating all along, anything above a 22 Mag or something in the .375 and above class?
Thats where your "Stopping Power" comes into play. It is better known in our "Redneck" world as Kenetic energy and energy transformation comes from resulting in the tear or crush factor from the Hydrostatic effect. Simply put, mass damage to affected and surrounding tissues resulting in immediate incapacation due to a properly placed projectile.
Third. In a perfect world, a heart shot does cease a forward assualt. BUT NOT ALWAYS!!!! I have both personally seen and been told about assailants that were heart shot with rounds from 308's that continued for upto 8 seconds after being hit perfectly in the heart. For immediate incapacation, the shot has to be delivered to the cerebellum or modulla oblongata.
So in all, its not is RedNeck BS.