I ran into a similarly infuriating issue with a hospital.

We have insurance. But we knew the procedure wasn't covered by insurance. So we would get the list price. We asked about the cash price. But they said we couldn't get the cash price because we have insurance.

They said that you cannot get the cash price if you have insurance because the hospital requires procedures always go through insurance if you have it. But we could lie and claim we don't have insurance. On the day of the procedure, they said, oh, if we bill it like this, your insurance would cover it! Sounded good to us.

They were wrong. So we ended up with the list price.