The limitations period on a written contract in California is four years.

You likely contracted at the time you received services that you would pay the bills if your insurance coverage was declined, or they otherwise went unpaid. It's hard to speak to your rights without reviewing the contract - but doctors and hospitals typically have patients sign a contract to pay for their medical care before administering treatment. The collection firm is probably proceeding on the basis of your statement of account.

Beyond suggsting that you continue to try to get Medi-Cal to pay the bill, all I can really do is suggest that you have the documentation you received reviewed by a local lawyer (or, if you are not able to afford one, perhaps a legal aid office) for possible defenses.