It takes an Act of Congress to trade or sell USFS Land... It is done, but NOT often... It usually takes Years to negotiate a deal... Alaskan Native Corporations have logged off a bunch of their Deeded Land, and now want to trade the Logged land, for Old Growth Forest USFS Land in the Tongass National Forest... They have been Lobbying heavily for years to get ahold of UnLogged Land... So far NO DEAL but it will happen eventually....
I haven't got a clue what that means. If they own it, it's deeded in their name same as any piece of real estate, and recorded at the court house Registrar of Deeds office. I went there and pulled copies of the deeds for the two different tracts that bound the sides of my place.
And that may have been the case in the trade I mentioned. I honestly can't tell you the details, other than I remember it happening (about 20 years back) and the paper making a big deal of it. Likely was a Congresscritter involved in it. As I said, the FS owns more than 50% of the county land (small county anyway), and the county has always moaned about the lack of property tax revenue because of it, even though they do get a "payment-in-lieu-of-taxes" check from the feds every year. I guess that payment is base loosely on undeveloped forest land, and not what the county could rake in off something with a building on it.