I don't think we need to posit a mustache-twirling villain here. They call it "skin in the game" because the idea, stated in plain terms, wouldn't be popular. If you strip away all the performative outrage that was the big "revelation" of John Gruber talking about why they started calling the individual mandate in Obamacare a "fine" rather than a "tax"; why wouldn't the same logic apply here?
But don't take my word for it; here's the Rand Corporation offering a studiously even-handed assessment and giving a definition of the term matching the one I suggested: https://www.rand.org/pubs/research_briefs/RB9672/index1.html
> These plans are intended to give consumers more "skin in the game" — that is, to make them responsible for a greater share of spending. Proponents of this approach contend that consumers in such plans will have more incentive to make prudent, cost-conscious decisions about using health care, which, in turn, should drive down overall health care costs. Critics, however, have voiced concerns that consumers lack information needed to reduce spending without reducing quality of care.
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> We don't keep the three grand we save by saying, "Hmmm... maybe I'll just lose 15 pounds instead." That's how things are supposed to work.
Well, first of all, that's false, in the sense that, increasingly, deductibles are substantial (a few thousand, at least), co-pays are higher, and co-insurance (where it's difficult to even predict what you'll owe) is becoming more common. Almost nobody has a plan where they don't have to pay something for medical care.
But besides that, maybe in your scenario someone decides to lose weight. But let's think of another scenario. I start to experience some pain but I haven't really got the money for the doctor's visit. I decide I can tough it out. I keep doing this until the pain is truly unbearable and then I go to the doctor and find out I'm terminally ill and I waited too long to be treated. Or I forego preventative care and miss an opportunity to catch and treat cancer early. There aren't outlandish scenarios; they're the result of a system where patients have to shoulder more of the cost of care out-of-pocket, especially when combined with a state of affairs where a great many Americans do not have the savings to pay an unexpected expense of a few hundred dollars out-of-pocket.