Everything you said lines up with the United States Forest Service except for the last part, about hiking paths, shelters, etc: here, those are under the roof of the National Park Service. While everyone is allowed to access national forests (excepting temporary bans when fires are a high risk), amenities making it easy and safe to do so are limited to park lands.

Back to the beavers, however. I assume that it would be these "other entities" you speak of that would be building and repairing the amenities and that these warnings are intended to aid those projects...I was going to ask why they would need a sign since the government should know who their contractors are and how to contact them, but then I realized that putting up a sign could be a good backup for when those contracts change, or for when someone forgets to send that email. Well, I guess a metal sign pole would have been a better idea...