I had my surgery in the US, but I paid for it out-of-pocket. I had rare complications 2 weeks after surgery that resulted in a week's hospital stay and a lot of expensive, on-going follow-up care.
My insurance company was billed for all treatments I have received for my complications and they have not balked at payment. They've even paid for a couple of blood tests as part of my VSG follow-up-- I think because they didn't realize that the blood tests weren't ordered as the result of the complication.
I guess think of it this way: if you made the choice to jump out of an airplane and hit a tree on the way down, the insurance company would have to pay for your injuries, even though they wouldn't pay for your plane ride. So even though they won't cover your surgery, anything that happens to you afterward is their responsibility.