I don't know the current (post-ACA) situation, but the short answer about the US's emergency care laws is "sometimes".

For instance, suppose you trip and fall, and in catching yourself, shatter your shoulder joint.

The emergency room would be obligated to keep that from killing you -- making sure the bone fragments weren't going to sever an artery or anything, stitching up open wounds and the like.

The emergency room would not be obligated to restore you to (as much as possible) functioning. If you need an expensive 20-hour surgery with a team of specialists to put all the pieces of your shoulder back together, well, that's too bad. Sure, your shoulder will heal into an immobile lump without treatment, but it won't kill you, so not actually an emergency.

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.

Sometimes they do. A person at my mom's work need an organ transplant, but they denied them the surgery because their finances didn't show they could afford it, let alone the medicine you need to take for life after that to fight off rejection.

I really don’t know. They usually say everybody gets treated but I would guess quality will suffer. Or you will get relaxed as quickly as possible.

Be ready to spend months or years on the phone fighting with the insurance though. It’s not uncommon to receive a $300k bill that you then have to clear up with many many phone calls.