I have a B CDL w/ no restriction. It's good to err on this side of caution. These posts come around often and I give the same advice. My take is, yes, it is the law in CA to operate these truck with such credentials and you don't want to get caught with "your pants down" if there is a catastrophic incident involving your truck and you. A civil lawyer, if you end up in litigation, will question your training, experience and proper documentation in the use of your truck. You may also be held criminally liable if there was negilgence on your part. Sorry to cast a gloom, but we have to roll safe.