I don't think that's true. I think that's actually the vast majority of people. Nearly all of them, even. The human survival instinct overrides so much of a human's rational thought processes or even their higher-order emotional processes. You may be one of the rare few for which that's not the case, but, well... you're of a vanishingly rare breed.

And it's not even exactly that. When you're in a life-threatening situation, it's likely that you're either a) unconscious, or b) completely unable to have even a remote grasp of what the cost will be to "fix" you. As in, not even a ballpark figure. Given the potential urgency, you may not have the time to get a second opinion or shop around for a cheaper fix. Just the cost of stabilizing you to the point where you can sit back and make an informed decision could bankrupt you.

Also, just a side note on:

> ... the welfare of their family

There's also a cost to their welfare if you die, too. It's hard to put a number on that while you're healthy, let alone in the midst of an emergency or life-threatening illness.