Bears will usually avoid people. Even if they come into the camp site at the first sign of human movement they will have a tendency to flee. So bear reports near a camp ground wouldn't worry me so much.

If however, mountain lions were reported in the area, that would worry me to the point of denying permission to go camping. Mountain lions although also likely to avoid human contact, are far stealthier than bears. If a bear wanders nearby, you'll hear it before you see it; while a mountain lion could be on the tree branch above you and you wouldn't know it. So the risk factor for having a dangerous encounter with a mountain lion is greater than with a bear.

That said, I've been camping 3 times in areas that are a habitat to bears, once in Yosemite, and twice in the Sierra Mountains in Chihuahua, Mexico. I saw deer, squirrels and raccoons. The closest I came to a bear was when someone pointed out some bear paw prints and supposed bear droppings.

The difference in danger levels between mountain lions and bears was given to us by a "viejito" camping guide in Mexico. His information seemed logical to me.