I've encountered hundreds of black bears in the sierras. In all of those bear encounters/sightings only two have been butt puckery, and it was both time a sow with cubs I didn't see. Both times I bumped the bears and the cubs, instead of running off with mom, went up trees. Mom of course won't go too far and when you do the normal yell or throw rocks the mom "runs off" but comes right back. I finally realized it was a sow protecting and not a bear that wanted me for lunch and I backed off and got quiet. A few min later I see the cubs climb down out of the trees and off they went. This makes it seem like you have a "problem" bear in the moment when really you've treed her cubs and she wants you out of there.
99% of the time they will run off and I've never carried spray. I do normally carry a pistol when backpacking but if I'm hunting in non-grizz there is no need for pistol since I'll have rifle or bow.