Public trees, owned by us. You can also camp anywhere you want in the National Forests, although they do limit your stay for a couple of weeks, then you have to move. At least on paper. Knew someone who lived in the Chippewa National Forest. He would just move to a different spot every spring and fall with his wall tent and wood stove.
I know most of the personnel who work with the Chippewa National Forest. Of those I know, there isn't one of them who would give anybody a hard time about climbing the trees, unless they were doing some serious damage. I don't know how it is in other National forests, but I would assume it is pretty much the same. Very nice and easy people to get along with.
Only time you run into bureaucratic tape is when you do work for them. Then the red tape is overwhelming.