Wow. They did that without even talking to you first? That’s rather inconsiderate.
Legally they are within their rights. Anything that hangs over onto someones property they can cut it off.
They are just being A-holes. When this was a brand new developement her dad would sneak out at night (we caught him as our house was being built) and collect lumber to cut into 3 inch strips and then he put up a fence with 2 inch gaps between. So he was able to see everything when we were outside. Usually people ask each other to go halves on the cost of a fence. In order for them not to see everything we put up another fence our side of his.