I swear, some people would argue with a fence post over what kind of wood it's made of.
Your state can say whatever they want about the subjet, if the US were good at environmental stuff it would be known by now (they aren't).
So you're a wildlife and ecosystem scientist? If you're not, what makes you believe that you know more than those who dedicate their entire careers to this stuff? In a survival situation you aren't going to chop down every dead tree in sight, and if they are not overly concerned about the loss of one or two dead trees obviously it's no big deal in the long run.
Black bears are one of the smaller kinds of bear, we have a few in our area so I've seen them around. A bear's skull is indeed pretty thick, but living bone and dry bone are two different things, dry bone is a lot harder. There have been multiple reports up north of even a smaller hatchet to the head killing a black bear. There are reports of a 5" knife being used successfully in bear defense, obviously not against the skull but it did work. I wouldn't want to try it myself. I'd have more trouble believing the stories about the people who strangled a bear to death empty handed.
In the woods, saws seem really effective. They cut dry wood rather well where even an axe struggles. I may be wrong, but it seems like they can be somewhat fragile if used carelessly. If they go dull I'm not sure how you'd go about sharpening them quickly. I can't say I wouldn't take a saw, but I wouldn't rely on a saw alone.
When it comes to fires teepee really is a great way to do it, I've had more success with that method than others. Fire isn't the only thing you'll need to be concerned with, shelter is probably the most critical if you aren't carrying a lightweight tent. A lot of times even a big knife can cut sticks to make a shelter. Having a dry place to store tinder and kindling to allow it to dry out is critical.
I'm not a wilderness survival expert, I'm just a guy surrounded by natural resources and a willingness to learn. I am human and have made my share of blunders that sent me packing back to the house. Even if I don't know what does work, I can share some experiences of what doesn't work.