Many inexperienced shooters would aim for that obvious and easy target. All they would do is pass over the actual skull through all of that inert flesh.
A stopping head shot should be aimed at the mouth or lower jaw, since the brain stem and the brain cavity is much lower in the head of a Brown Bear.
The use of shotguns with slugs has been proven in an earlier USGS study to be completely ineffective on Brown Bear. They determined that Slugs cannot penetrate the head and the skull or the body of a Bear with lethal effect.
Was this a typo, or did you mean to say the 12 ga wouldn't work?
In my youth, I shot at a range with all manner of crap left on it - Dishwashers, Tv', etc. I remember hitting a cooking pot left by someone at 30 yards with a simple 2 3/4" hollowpoint lead slug. I figured it would pancake and dent the pot, as the pot was a much harder alloy and about 3/4"-1 inch thick on the bottom - but the slug blew clean through. With slugs today being saboted, and made of unique alloys that are harder than lead, and especially with the specialty rounds you can get, I would think a modern 3" or 3 1/2" saboted slug would be as effective as anything for head shots, if placed right. Not that I know anything about bear.
I remember outdoor life doing a piece on a guy who offed a Grizzly point blank with a .22LR pistol to the noggin. On the necropsy, out of twelve rounds or so, a whole bunch had found brain.
If the 12 ga doesn't work reliably, do you know why? Anatomical issue?