That's not how insurance works. They aren't going to pay for stuff on the say so of one doctor. The expectation is that they pay for treatment according to published and accepted standards of care. In this case, those say that you can fly with broken bones.
>With all the responses you've generated here and the way you go about your argumentation I wouldn't be surprised to find out that you work for the insurer.
Of course I don't work for the insurer. I am just an experienced backpacker that understands the concept of travel insurance.
> It's crystal clear from the way they conducted themselves that the insurance company would find any excuse to deny his claim
I see no evidence of that. What they offered was exactly what travel insurance is there for. That is, travel home for further treatment after a patient is stabilized. OP wanted to argue he wasn't stabilized. In response, they told him specifically what he needed to get from his doctor in order to justify his claim. As far as I know OP, for whatever reason, never bothered to get that.
IMHO, it's debatable whether or not you should be travelling with unset broken fingers. However, if all you bring to your side of the debate is a single sentence, you're going to lose.
We also don't know what their reaction to paying for the emergency services would be. OP, for reasons that are clear only to him, has decided not to claim ~$6,000 worth of covered expenses.