You’ve given us very little to go on, a few lines from a news article. I’m speaking from 24 years of Navy service. Whether your wife has the paperwork that says the Navy can do this in hand or not, the Navy can do this. JAGS are nothing if not risk averse. That they are being so inflexible in your case is telling.
I’m surprised the Navy is requesting all the money upfront. In my experience that not how the Navy handles indebtedness, although I have heard of other services, specifically the Army, requiring immediate, full payment for indebtedness, although not repayment of tuition.
In only one instance have I ever heard of tuition repayment being demanded by the Navy, and that is in the case of a young woman who went AWOL and hopped a plane to see her boyfriend without telling anybody where she was going. She was thrown out of school and the Navy and immediate payment of tuition was demanded. So the fact that the Navy is taking such a hard line leads me to think that 1) there’s a WHOLE lot more to the story than we’ve been given, and; 2) somewhere along the line your wife ticked off the wrong person and/or gave someone in her chain of command or the medical chain of command reason to be angry with her. I’m not accusing anyone of anything, but I am saying that in my experience what the Navy is doing to your wife is unusual bordering on unheard of, and things like that aren’t done without reason.
My advice is this: neither suing the Navy (good luck with that!)nor declaring bankruptcy will accomplish your goal. I think you and your wife need to keep in mind that the Navy has the upper hand here, and conciliatory tones and and a kindly offer to work with the Navy to lower the amount of the debt and get favorable repayment terms are the way to go. Start with a FOIA request and get ALL the paperwork the Navy has about her case. The FOIA won’t make you any friends, You may be able to figure out the rest of the story that way. Get a good attorney who was a former Navy JAG, one who worked with medical boards. And good luck.
Of course, the Navy has the upper hand. The Government always has the upper hand. After all, it's the Government, and it's bigger than you, has unlimited resources, and unlimited manpower, and even if you're in the right, by the time you've successfully fought off the hordes of bureaucrats, the damage is already done.
I had an Army scholarship, and I echo your sentiments 100%. I knew guys who couldn't fulfil their obligations for medical reasons (usually injury, not illness), and they were simply released from their commitment for the good of the Army -- no harm, no foul. The Army typically doesn't use the "pay up or enlist" option unless the cadet has *really* screwed up.