My Lyme doc is out of network for all insurances ("doesn't take insurance"), and yes, after I meet the out of network deductible, I do get about 40% of the cost back. The dr's office will do the initial submission to the insurance company, but nothing more.
I have had more costly issues with (lack of) coverage for the prescriptions, because most of them have limits on the number of pills that the insurance will cover in a given period of time. For example, azithromycin was covered for 6 pills every 28 days (and of course, "covered" means they will pay their part of it). I needed 24 pills every 28 days, so I had to pay the full cost of the 18 that were over what the insurance company determined was sufficient. And that was 1 of 4 drugs in my regimen.
Last visit my dr. prescribed a month of a relatively new drug (maybe 5 years old) to see if it helped (so, sort of an experiment, not a critical component). It's only insurance-approved for 6 pills (3 days worth, which is 1 weeks dosage) every 25 days. The drug turns out to be $50+ per pill so I am collecting 4 weeks worth one week at a time every 25 days. I consider this a ridiculous necessity: it's $22 for a week's worth with the insurance coverage, $317 without. Fortunately this is a drug I can wait to try and not something I needed immediately, since $1300 out of pocket is absurd!