I'm somewhat under the impression that depending on what happens when you tell your situation on the phone, some doctors will be willing/not willing to help you if you have already gone to a different doctor for the surgery

What kind of reasons will let you use USA health insurance on the nail removal and which kind of reasons will force them to say "sorry, that's not a legitimate reason, you need to pay out of pocket without insurance"? 

I'm doing gnail with Dr. Giotikas now and thinking about what to do down the line

For out of pocket, I am not sure if flying back to Dr. Giotikas is cheaper than doing with it with Dr.  Assayag. I can drive a few hours to Dr. Assayag (be driven I guess) or fly to Athens from D.C., not sure how this works out in practice for the better option considering price. I know that Dr. Parihar refuses to do nail removal for people who are not his patients so at the moment I am trying to figure out between Dr. Assayag (closer to where i live in the USA) and Dr. Giotikas (my current doctor). For certain it depends on the health insurance but I'm quite hesitant to ask my health insurance company about this and am not sure how to figure it out on my own, I somewhat wonder if there is a health insurance code for nail removal and its standard costs