Back to the original concern, for whatever it's worth, here's my story:
I've been in the woods off and on since I was about 10 (I'm 77). I've seen a great deal of large wildlife over those years, and been aware of more. I actually walked up on a couger on the ground and was so startled I forgot I was not supposed to look it in the eye. In about ten seconds, the cat took off on a series of beautiful, fluid leaps, tail flying, and was out of sight on the third one.
I've seen bobcats, mostly as balls of fur headed the other direction, fast. I've seen a number of bears, again, mostly fur going the other way, though I got caught between mom and cubs once. She was so close I could smell her, but she didn't even threaten to bother me. I saw another sending her cubs up a tree, but again, showed no interest in bothering me. I've never had a bear bother my camp (I tend to be by myself and away from regular camps, also, I should say that all of these have been the relatively small and shy Eastern black bears, no griz).
I've seen hundreds of deer, and never been threatened. The only critter that ever actually attacked me was a moose. He hit the tree that I stepped behind, shook himself off and headed back to his pond (yes, it was rutting season).
The only other critters that have scared me are skunks and drunken redknecks. Caution and common sense (as others have noted above) is appropriate, fear is not.
But a couple of provisos: Bill, when I was a kid, we'd hear the big cats and bring the goats in. They never got any of ours, but a neighbor had sheep and lost several, very close to their home.
Also, Tim Ernst reports in the Highlands Trail guidebook that a backpacker on the trail was attacked in his tent by a bear, but survived. Ernst says this was the only reported bear attack in Arkansas. Again, caution and common sense.