I have Anthem BCBS of IL. I think the state/region matters. Ours covers bariatrics. All we have to show is that we made an attempt under a doctor's supervision (typically it's 6 months of monthly visits and weigh-ins) and a letter of necessity.
Pretty sure Anthem is the trade name for California BCBS. Their policy statement is here, but it's not too clear on whether or not you need a physician supervised diet.