Here's the thing, though: Most of the time if a grizzly knows a human is around he'll avoid the encounter if he has a choice....that's not always true with a dog in the equation. Dog smells/hears grizz, or vice versa, and there's a conflict.
Denali National Park has a high concentration of bears AND a lot of backcountry users. They've had exactly one bear attack since 1983, and it only resulted in minor injuries. Everybody who goes into the park's backcountry gets a detailed briefing on how to avoid bear contact, and is required to carry their food in a bear-proof container. If they don't have one, one is provided. The bears don't associate humans with food, and pretty much ignore the humans they come into contact with. The program seems to be working.
But Denali is a very special case, I think. The Park has succeeded in isolating and effectively training their bears not to associate humans with food. This is good, but atypical. Elsewhere, throughout the backcountry, bears do make this association, unfortunately.
Please note I said dogs, plural. I wouldn't like to go into grizzly country with only one dog. Bears will flee from a pack of dogs every time, not because the dogs pose any immediate danger to the bear, but because they just want to get away from the noise and confusion after seeing they are not going to be able to catch one of the dogs.
If the bear doesn't flee, the dogs will literally "hound" them to death.
Of course, your dogs have to be trained to break off the chase on command, else they'll end up scattered all over the wilderness, with perhaps some of them dead. Definitely not a job for your typical couch potato pooch.
The advantage of taking dogs with you is that no one gets hurt. Not the dogs, not the bear, not you.