Medical Group Won't Bill Primary Insurance?

Having some issues w/ billing with primary and secondary insurance in California. This is for my daughter. Hoping someone has relevant information to share.

From what I read online, I thought it would be standard practice to bill Primary and if Primary doesn't cover it, bill Secondary and if they cover it, they'll pay it.

But, maybe that was ignorant of me. There doesn't seem to be clear information on HMO Primary and PPO Secondary insurance scenarios.

We've had Kaiser, but they don't cover specific food allergy treatments we want for my daughter. So, we picked up a PPO health plan (AETNA, MHBP) though my wife's job that does cover it (on top of Kaiser due to established speech therapy).

The Allergy department said to get a referral from Primary. We went to a primary physician in the same Medical Group, no issues so far. They even sent out some labs for another medical item. But, when they sent in the referral to the Allergy department, the Allergy Department flat out rejected the referral because Kaiser is the primary (even with knowing that AETNA is secondary)

We were not expecting this. We called AETNA, they said there shouldn't be any issues billing Kaiser, getting rejected then billing AETNA. Called Kaiser, they said they never heard of anyone just rejecting the idea of billing Kaiser first.

Question, is this scenario common or is this something unique to this Medical Group. I spoke with numerous people in the Medical Group and got conflicting information, but ultimately spoke with a rude "Patient Advocate" who said it's the Medical Group policy to not bill Kaiser even when there is a secondary insurance that will ultimately pay ("we don't know if they'll pay. . . "). And, that it was an oversight that we were even allowed to see the primary physician in the first place.