Back before the Affordable Care Act took effect, a lot of the health insurance horror stories I heard had to do with short-term health insurance policies. They were typically purchased by people who thought they were getting a really good deal since the policies tended to be cheap.
Unfortunately those policies are generally not renewable unless you stay healthy, so a serious illness or injury near the end of the policy's term could leave the patient suddenly uninsured and back then uninsurable. On top of that, such policies typically provide limited coverage and cap how much the insurance company will pay out. There had to be some reason the policies were so cheap, and that's it.
Under a full Affordable Care Act (Obamacare) policy it's the patient's spending that's limited, not the insurance company's.
The Affordable Care Act did allow temporary short-term policies to be issued, but only for three months, as a way of helping people get at least some inexpensive insurance between jobs. But now the Trump Administration has authorized "short term" policies for as long as a year. This can again lead naïve consumers to buy such bargain-basement insurance under the mistaken impression that health insurance is health insurance. (Others might buy them even knowing the coverage is skimpy because they're convinced that since they've never yet been seriously injured or ill, they never will be.)
Here's Dr Aaron Carroll on the subject: