I am no fan of arbitration agreements and the trend of avoiding courts for big corporations. But in this context, simply as a technical matter, arbitration is within and subordinate to the legal system.

You can sue anyone for any reason at any time, period. The degree to which you might succeed depends on laws. To the extent a contract demands arbitration it's because it is a contract, which is defined by the legal system. The system of arbitration depends on those laws to be effective, and the backstop for it is always the courts.

This isn't true in the reverse. Congress could outlaw or limit arbitration tomorrow. No arbitrator could dissolve Congress.