Might be two different incidents.
The one I know of happened in '87 or '88 in or around Glacier Park, and the guy knew it was a big grizzly. The reason it got filmed was that the annual conference of the Outdoor Writers Association of America was being held in Kalispell, and the bear guys asked if any of the writers would like to watch and film a grizzly being released from a trap. Didn't work out quite like they expected.
By the way, the bullet that killed the bear was the last in the 6-round cylinder. The previous five had all hit the bear in various places, but didn't penetrate anything vital. In fact at least a couple hit the skull and then slid off between skull and hide to end up at the back of the head. The 6th went into the bear's mouth and throat, and broke the spine.
I also heard, however, that the bullets were typically soft 158's, not really designed to get inside a big bear's skull. There are .357 bullets today that will do that job, however.
I was fishing in Alaska in 2008 in an area with LOTS of brown bears. The closest encounter was with a big female that came out behind us on a gravel bar and wasn't happy about it, partly because she'd just been chased downstream by a nitwit woman who was trying to take her photo with a point-and-shoot.
Our guide was a very well-known brown bear outfitter from the Alaska Peninsula. The bear was 15-20 feet away and the guide whispered for us to just stand still. Meanwhile he slowly drew both is big can of bear spray and...his .357 Magnum.
Luckily he didn't have to use either. Since we stod still and didn't threaten her, the sow eventually just turned away and left.
Since this guide has seen LOTS of big bears taken over the years, and is a very savvy gun guy, I would guess that whatever load he had in the .357 had been tested on bear skulls.
And the other side of the deal is that with any handgun, at close range the only real chance you have is to put one in the brain.
