I'd like to know other non-US citizen's opinions on your health care system are when you read a story like this. I know there are worse places in the world to receive health care, and better. What runs through your heads when you have a medical emergency?

A little background on my question:

My son was having trouble breathing after having a cold for a couple of days and we needed to stop and take the time to see if our insurance would be accepted at the closest emergency room so we didn't end up with a huge bill (like 2000$-5000$). This was a pretty involved ~10 minute process of logging into our insurance carrier, and unsuccessfully finding the answer there. Then calling the hospital and having them tell us to look it up by scrolling through some links using the local search tool on their website. This gave me some serious pause, what if it was a real emergency, like the kind where you have no time to call and see if the closest hospital takes your insurance.