Can't say I'm too fussed about impoverished people getting a few boxes of diapers, and using ambulances for transit reveals an underlying societal problem more than individual greed.
If people are willing to go through that much trouble just to get from A to B or to save a few dollars on diapers, there's something wrong.
They're investing hours and go through quite a hassle just to possibly save single digit amounts of dollars.
You don't do this if you don't think you have to.
The ambulance rides do tie up the system however. I have a cousin who is an EMT and between rescuing overdoses he has regulars they have to taxi because they have a cold, or something else trivial. There is public transportation, but even that would cost them personally and requires waiting. It's probably better to let a few selfish people take advantage of the system in the long run, but it amazes me how selfish some people can be when there's people in real need out there.
Costs for various treatments are already negotiated ahead of time and hospitals/doctors bill insurers directly.
If the insurer thinks you received some kind of treatment you shouldn't have, it's between them and the hospital/doctor.
Of course there's always the odd/fancy treatment people insist on getting that is not covered. In that case you'll be billed by the hospital.
In neither case you'll be fighting any insurance company personally.