Who made the mistake? My provider’s office, or my insurance company?

I recently had extensive diagnostic labwork done, but received a $966 bill with an EOB stating that it would all be applied toward my deductible. Per my Summary of Benefit Coverage, diagnostic labwork is 100% covered. I’ve spent a total of about 15 hours on chats & calls with my insurance provider as well as my doctor’s offices to understand why I’m paying anything. I’m getting mixed answers from my insurance company – one agent told me that the CPT codes used for the procedures are causing the issues. But another told me that the place of service code was the culprit (would have been fully covered with 11 – office visit, but is not because it’s 22 – outpatient facility). My question is – can my provider actually change the codes they use? They’ve said they cannot change the place of service code. Is that true? Can they change the procedure codes? Are there multiple codes for the same procedure?

I’m worried that if I appeal the bill through my insurance company, I’m going to wait months to get the same mismatched answers. I feel like I’m getting the run-around and being told by everyone “that’s not my department, call these guys” perpetually.

I appreciate any help or insight!

(I’ve also asked what I can do to prevent a surprise bill like this in the future and was told to call in advance with the NPI, TIN, CPT, and Place of Service code before each visit. Sounded easy enough, but I spent another 3 hours on the phone with my providers office & their billing department to get that information).