I just looked up cougars -- I was trying to get a feel for the lynx/cougar differences and I found this article from just a few hours ago about a dog that saved a kid from a cougar. http://www.cbc.ca/canada/british-columb ... ttack.html
The attack was on the mainland but the most cougars are on Vancouver Island where there are no wolves or coyotes to compete with them.
Cougars and lynxes behave quite differently with regard to humans. I don't think even the most fanatic hunters or safe-wilderness-oriented people here have seriously accused lynxes of attacking people, only possibly of taking a cat or a pet dog.
Deer seem to be moving into town where they can't be hunted and...
Deer and boars are, to be truthful, pests when allowed to increase without restrictions. The hunting season doesn't cull them sufficiently, but as noted, lynxes aren't allowed to compete with hunters (one has to be sure of a good next hunt, after all ...). Moreover, deer have lost their normal shyness for humans - as you wrote, Alice, they happily move into settled environments.
This is probably the greater problem with many "wild and dangerous" animals: not yet, but if they really change behaviour and lose their natural shyness. Some - like bears - seem to do it easier than others, like wolves and lynxes. Our way of living may well encourage such changes unless we are prepared to consider and take some trouble in and with nature.