I broke my wrist on a recent trip. After waiting overnight in an ER with out seeing a doctor until the morning, I had already decided I wanted to go home for surgery. The doctor provided pictures of X-rays (which he took with my phone). He wrote up a note saying which bone I broke, that I needed surgery and that due to not being a local, he recommended I return home for surgery where I could follow up with my own doctors and follow up care. This was important - he needed to indicate that I was "fit to fly". The negative in this is that he put me in a cast. After I was released, I called insurance and they would not let me fly with a cast. So I had to return and have the cast cut.
I submitted all the paperwork to the insurance company in order for them to arrange flights home (with a medical escort). I did not have to pay up front for my medical care (hospital took a picture of my passport).
Once I got home, I got a copy of the charges and submitted them. I did not use the forms from the insurance company. I had a claim with Allianz (land portion) and Aon (cruise portion). Both took the the doctor's note and did not require their form to be filled out.
Previously I used their form when I cancelled a trip before the vacation.