Maybe they're concerned some catastrophic injury will befall them with no other party being responsible, and they'd have to pay out of pocket for it. I don't think Obamacare is so efficient that you can sign up on your smart phone before you bleed out from a large puncture wound.
In such an event I would only need to pay for the immediate ER treatment to sew me up and stop me from bleeding to death (they'll bill me later). If I then sign up for Obamacare's gold plan I can use it to pay for any ongoing physical therapy/internal surgery/organ replacements/prosthetics/etc I need, where the bulk of medical costs are incurred.
Finally, once I am done with my treatment, I can simply cancel my insurance.