The vast majority black bear sows with cubs will not attack a man, even when the cubs are bawling for help.
This was shown by bear researchers as they routinely handled black bear cubs in the wild.
There are a few exceptions, of course, but they are very rare.
If you run from mama or try to climb a tree, you may trigger the "fleeing prey" or "fleeing combatant" instinct.
Fred Bear wrote about this very subject in one of his books.
Steve Isdahl has a funny story about a black bear on his front porch. Look him up, I gotta go to work.
Yes, black bears are definitely far less a threat than grizzlies.
I’ve had two (known) encounters: one at 10 feet, and another at 40. The first passed in the opposite direction on a narrow path and the second ran up a tree when my neighbor’s dog barked at them. Two large black bears TOGETHER are typically sister-bears. (There were two bears—I saw only one—and it was BIG).
‘Glad my mini-dachshunds weren’t there. They would have chased after the bears!