When does a dental issue become a medical issue?

Backstory- February I had a tooth removed (top molar). In doing so a hole between my sinus cavity and my extraction site was created. In May it became infected, had to get it drained and the surgeon said he expected it to heal and close up on it’s own. In July it hadn’t healed, so he said I need to have surgery to fix what has become a fistula and I may not be able to get the implant I was wanting if the bone grafting does not take. I get the estimated cost (which includes the implant I don’t even know if I can get) and am expected to put half down before I can schedule the surgery. I have dental, but they cover very little.

I contact my health insurance (fepblue) to see if it’s something they can help with, because I will be put under general anesthesia. They say yes, as long as my surgeon provides information that it’s medically necessary. My surgeon’s office is basically refusing (at one point they said it was not medically necessary) because health insurance doesn’t cover anything in the mouth so what’s the point (at least that’s my impression).

This past weekend I got another infection and had to go to the ED to get it drained and on new antibiotics. So… it seems necessary. Is insurance just okay with footing an ER visit every couple months instead of fixing the issue, or is my surgeon’s office just being obstinate and not willing to put in any effort?