No, they cannot deny essential treatment in the US due to financial issues. The type of treatment can be argued about and fiddled with (elective surgueries and whatnot, prisioners needing co-pay money they do not have, etc). But in a life-saving case like the one in the article, they cannot not deny treatment. As another example, if you need a C-section, you are getting a C-section.

That said, fiscally, it's a total gamble in the US these days. You may be saddled with a $20/mo debt that will likely never end ever, or you may be facing a bill for $1M that is due in 30 days. The range is essentially unbounded and unknowable in any real way.

US healthcare is shockingly cruel, financially speaking.