You believe you own and I own federal land?
So we should be able to enter any federal land any time we want?
You should try that sometimes and see what happens.
Considering I've been all over federal land in at least 20 states including Utah, yes I really do think federal land is owned by all Americans, subject to some restrictions. Outside of National Parks almost all federal ground is free to enter, camp, fish, etc. National Parks charge to pay for the services provided to the visitors and to pay for protection of the park.
I hike about 1000 miles a year. I'd say about 75% of it is on Federal Land, 20% on city land, 4.8% on state land and 0.2% on private property. Basically anything longer than 5 miles is on federal land, private land is generally just a few hundred yards to get to the federal land. State trails of any length or significance generally dump off into federal land pretty quick to.
National Forest land is particularly accessible in states like Arizona due to the abundance of mining/lumber roads and the mild climate allows for pretty easy travel upon them.
You can camp for free and the Feds will even give you a map.
Quite a nice feeling being camped on the edge of the North Rim of the Grand Canyon with a fire ring and an already cleared tent pad.
Even in the limited national forest land in Oklahoma, there are a ton of trails, with easy access, free camping. Last year we had a pretty bad ice storm, a few month later I called the rangers and got a full trail report. The state parks pretty much have no trails and the ones they do have are barely maintained.
You can also get a permit to cut trees, hunt, etc on federal land. Doubt you could do that on Georgia-Pacific's "forest." Hell I was ready something the other day that everyone in Oklahoma could go harvest a Christmas tree for themselves for free.