They can write whatever they like; state law dictates how it actually proceeds.

In my state, you must start with arbitration but you have zero obligation to accept that decision and can sue regardless of outcome.

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.)

Fair, but I was speaking more generally.