Are you in the U.S.? There is precedent that has helped create laws to protect people whether they're adults or not, disabled or not, from what I personally feel has happened and is still happening. Seeing as how I know they read this board, I am not going to delve deeply into what I am gathering, but try to skim through U.S. law and state law.
Yes they could probably have launched a legal action to get their son declared incompetent to manage his own affairs. They could have been appointed his conservators if - and it's a big if - they had won that suit. The fact that they would probably have not won the suit being set aside, let's look at a few things.
~The cost of doing this in legal fees alone would have been astronomical.
~It would not have been a process that could be undertaken without months and possibly years of legal wrangling.
~The breach it would have brought about between themselves and their son would have been insurmountable. So had they lost - and they almost certainly would have lost - they would have been cut from his life entirely.
~If there is one thing we've learned about Hannah and Shane at this point it's that they have some masterful advice on handling PR and controlling the narrative. So his parents would most certainly have been painted as greedy, cruel, controlling monsters who were trying to prevent their son having a life independent of them. Their reputation, family bonds and financial security would have been destroyed.
I'm guessing they weighed all this up and decided that the path of least resistance was all they had open to them. Help him move, seem to acquiesce to it all and they might be allowed to be there when he needed them. They would at least be able to maintain a modicum of contact. Oppose it and they'd never have spoken to him again. In addition they would have been condemned in the public eye as selfish control freaks only out to keep a handle on the NFP even if it meant destroying their son's fairytale romance.
They were in an impossible position.