Most easterners know what they know about wildlife from watching Disney specials.
Cougars and bears are potentially dangerous animals - not cartoon characters. You are right on the mark about cougars and their stealthiness and penchant for children (or smaller adult humans). Normally, a big guy is in less danger - especially if he has a gun or a good knife with him and knows how to use it.
As for easterners and urbanites in general, they have a lot to learn about coyotes and other predators as well. Failure to 'defend' your turf only results in greater invasion, and greater risk of confrontation.
I grew up in Maryland, but a career as a geologist has let me travel all over. You either learn the local risks or end up a statistic.
I can't believe how many 'nature lover' types remain ignorant of the fact that there are critters out there who will regard them as a hot meal.