I don't think that is true in the United States. The Federal Arbitration Act applies nationwide, and it explicitly preempts state law.
If you think that I am wrong, please explain why.
(You are right that you "can sue regardless of outcome," but only in the sense that anyone can sue anyone for anything. If you enter into an agreement to arbitrate disputes, the outcome of that arbitration is generally binding.)
A lawsuit. That is what the legal system is for. But for some reason people seem to look down on this which I find baffling.