This isn't really true. You're going to get medical help with an urgent medical issue in any developed country, even if you don't have a penny to your name. Doctors/hospitals cannot turn you away for not having money.
There are also very few countries in the EU where insurance payments are $100. The only country I could think of would be Bulgaria and that's because they're the poorest EU country. Virtually everywhere else you're going to pay more than that and everybody has to pay it, including the poor. Depending on the country, if you don't pay that then you won't get medical care (other than the urgent kind) in those countries either.
The US has a lousy health insurance system. The cost is too high, insurance paperwork is ridiculous, and insurance doesn't always even cover you. But healthcare really isn't as amazing in most EU countries as you want to think. Many of them have similar problems.