This is an entirely reasonable concern and I agree with it. If you're not in the US (or you're young / otherwise don't know people with horror stories) it may not make sense to you, and yes, it's awful that it's realistic, but it's still realistic.
1. Coverage by medical insurance, in the US, does not generally translate to 100% coverage. For a variety of reasons, including coinsurance, copays, out-of-network coverage (especially common if there's some sort of emergency), in-network coverage beyond what's covered (e.g., the doctor says "this is medically necessary" and some bureaucrat at the insurance company says "I disagree"), and so forth, you can have a medical insurance plan and still be on the hook for large amounts of money.
(I don't think you implied this, but just to clarify, "making good money" is typically not strongly correlated with having good insurance. Because of how byzantine medical insurance is, it's hard for a potential employee to figure out what their offered benefits will actually cover, so it's generally not a factor in negotiations at all, unlike actual salary, and in turn higher-paying employers don't have a particularly strong reason to offer better insurance plans.)
2. You can have a "life-threatening condition" that is easily manageable via modern medicine. Take diabetes, for instance - life-threatening if unmanaged, but very well-understood in how to manage it. I have a friend with a chronic condition that requires taking an (expensive, only partially covered by high-tech-employee insurance plans) injection once a month. As long as they take that injection they're fine; their body becomes effectively unusable without it. I know multiple people who have beaten cancer; I don't think any of them would say that the actual process of beating it was easy (or cheap). The whole reason you care about medical care is so that "life-threatening conditions" stop being life-threatening.
Also, we have this pandemic going around which absolutely can be life-threatening, but even among the people who get very sick with it, many of them come out of it fine provided they have immediate high-quality medical care.
3. Beyond the assumption that the person you're replying to is treating family poorly... the amounts of money in question are generally larger than can even be pooled across many family members and large support networks, even if they all have substantial savings on their own. And even if technically I can manage to pay off a medical bill by exhausting my life savings and those of my extended family, what happens when someone else in the family gets sick?