Nothing. The proposition is very simple. If a contract provides that disputes are to be resolved by means of binding arbitration, and you sign the contract, you are agreeing to the contractual terms.
If you want to buy health insurance from a company that sells such insurance, and you sign the insurance contract and pay the premium, you become entitled to the benefits under the contract, including having your doctors' bills paid by the insurer. The insurer is bound to pay the bills according to the contractual terms. And if there's a dispute, you are bound to resolve it by binding arbitration, just as you agreed when you signed the contract.
Courts routinely dismiss lawsuits where the defendant comes in and says, "look, this is the contract between the parties; right here in paragraph 27 they waive their right to bring suit and expressly agree to binding arbitration."
Not legal advice as I don't practice law in California. It's just my two cents on the facts you describe in light of general principles of law. If you need legal advice, please consult a lawyer who holds California licensure.
Sometimes arbitration clauses can be challenged as unenforceable, depending on their exact language. In fact, these clauses were recently struck down in the credit card agreement context. But usually these clauses are enforceable and CA courts honor them, just as they honor most forum selection clauses.
As with almost all contract questions, no one on Avvo can guess what yours says, and no one can anaylze the terms and consequences without reviewing the exact language at issue. See a lawyer for help.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Sometimes you can ask if there is a version without the arbitration clause, but they may not offer one. The issue will come up when someone wants to sue someone or there is a dispute. There is a possibility that you could challenged the clause, but it is an uphill battle to get around it.
This answer does not create an attorney client relationship. Consult an attorney before you decide on a course of action. A review of all documents and a consultation at a minimum is necessary to render effective legal advice.