Not really, it's true that the truly asset-less actually does get taken care of in the case of emergencies. There are two major issues with this, however. One, many of these emergencies are the result of neglected chronic illness such as hypertension or diabetes. When you only address an emergency but not the chronic illness, these patients become what the hospitals refer to as "frequent fliers", repeatedly costing the hospital/government enormous resources to address emergencies when they could've been avoided with just some family doc visits and cheap generic drugs.
The additional negative effect of this is that these hospitals are nearly all for profit and have to fund themselves from the insurance payments. Treating the truly asset-less in emergency departments costs them so what they do is they charge more to those other patients that can pay, effectively increasing the healthcare financial burden on the rest of society. It would have been cheaper for everyone if the very poor had received cheap preventative care so that emergency departments do not have to do these expensive last minute patch jobs on someone that will likely fall apart after a short period of time. Someone who is asset-less is not likely to be able to regularly pay for the long term medications to keep chronic conditions like hypertension or diabetes under control. For the medical staff in these hospitals, it can be demoralizing as they see the futility of what they do unless there is longer term follow-up and care.