The East Wing

Perhaps this is stupid question, but I need to ask it nonetheless: Does the president of the U.S. have the right to do something like this? I presume he doesn’t have a deed to the White House. As such, can he sell it? Build a Pizza Hut on the property?
How is this situation different than my walking across the street to the park, where I commence cutting down trees because they block my view of the mountains in the distance?
I would expect to be in handcuffs within a few minutes. Why? It’s not my property.
