Although America's relationship with her tree house changes as she gets older, there's one thing that remains the same: it's still her sanctuary from the world.
When America was a kid, she and "Kota would tie up sheets to the branches so it looked like a ship" and pretend that they were sailors" (1.75). Pretty adorbs, huh? In this way, the tree house helped both Singer siblings escape the reality of life in Illéa's lower castes.
The tree house gets a lot steamier once America becomes a teen. At that age, the tree house becomes a "haven" for her and Aspen's illicit relationship, providing a backdrop for their romance and a nice private spot for making out (2.1). Nothing imaginary about that.
Now, necking with your bae is a lot different from playing pirates, but that's not the point. The point is that in both instances, America is using the tree house to escape some unpleasant part of her life and create a private world for herself.
Think about how different this feeling is from the feeling America gets at the palace. Logically, she should be way more comfortable in her new royal digs than in that four-by-four wooden box, but she isn't; she actually feels trapped in the palace. All this fancy-schmancy schmoozing just isn't her thing, even it's a dream world for many of the other girls. This is another reminder of America's complete distaste for materialism, a quality that helps her navigate the tricky waters of the Selection with her dignity intact.