It seems like everyone here is literally conjuring up first an agreement, and now laws out of thin air. What law is the state exempting itself?

Anyway tree law is super, super well-established and it works the same way for private parties. Your neighbor's trees are none of your business until they are on your property, and then they're exclusively your business (except you can't structurally damage or kill the tree e.g. by cutting roots that cross onto your property).

You clearly have some strange bone to pick. You should pick it elsewhere.