It's true that wild animals generally avoid trails because they mostly don't want to run into humans. More true of species that are hunted.

It's not the case that bears and cougars are on patrol looking for people to stack when nobody is looking. Attacks on humans are pretty rare. They've been more common in recent years but still not common overall.

Washington has black bears, maybe one or two grizzlies in the NE wilderness. Black bears are skittish and usually very frightened of humans. They can be trouble if they become habituated which is more of a problem near campgrounds.

I would honestly be more worried about breaking an ankle on a rock I couldn't see through the vegetation personally. Or getting cliffed out. That kind of thing. Not wildlife. But there are no guarantees.