I'm with Navy_Blue on this one without knowing all the details. It is probably the lack of private health care in this country that is confusing the issue. We generally work under the assumption that you get what you need free of charge. Therefore if you have to pay for it you don't need it. From that it follows that if you're suing it is for frivolous or punitive reasons.
In Britain they have a public/private system with some doctors being outside the system. If you want their services you have to pay for them. More often than not that means finding an insurance company to pay up.
In the US it is not uncommon for neighbours, friends or even family to sue each other, with no rancour involved at all, in order to get the medical coverage needed. A buddy of mine in the states had a 13 year old boy, by definition and idiot, who got a hold of some of his dad's black powder, a length of pipe and a couple of potatoes. He and his buddy thought the first couple of rounds went off just fine so they upped the charge and the load and the inevitable happened with trips to the hospital all round. Painful memories and a learning experience. Although both idiots were complicit in the activity Dan's buddy sued him to get the medical treatment that his son needed. Because it was my buddy's powder he won the coverage. My buddy was fine with this. The neighbour was fine with it and they still drink and hunt together. It was strictly a cash transaction.
That's the way I see this situation. The cadet has likely received treatment but has a scar. She has also likely gone to a private plastic surgeon who has given her an estimate on getting a better job done. This is likely to cover that cost.
And if any of you have ever had teenage girls or been a teenage girl then you can probably guess how important a scar on the face might be. Pimples call for couselling. ;D