I'm glad you are OK.
That said, my husband had this happen (Federal BCBS). He saw our in-network physician, who prescribed a particular test, which at the time was fairly new. We had never before been billed directly for a test, so didn't think to ask questions.
Eventually, we got a bill for the full lab charge, about $700.00. BCBS said, "Too bad, they used an out-of-network lab to read the results."
Nothing we could do about it, except vow to ask every physician, in future, about the provenance of every single test and lab that interprets the test. Just as you said - right there in the office, before they submit the Dr's order to the lab! Never mind if you are sick, possibly in pain, and worried stiff. Gotta do your due diligence!
Thank you for posting. That's exactly how it usually plays out. Consumer/patient is always at the losing end.
Anyway, now I wish this forum had a 'sticky' thread of what things to research before going to a doc, questions one should ask at a primary doc's or a specialist's office or even to how handle a process for lab work or imagining to avoid surprises later. Do we have something like that here? Would there any interest to have it?