What it does have to do is that the FDA won't legalize a lot of practices that are commonplace in most European countries. In fact, you could say in this regard European countries have a more free market in health care procedures than the US.
True, and the US has always been slow to allow new practices, treatments and drugs, both the FDA and ethics panels composed of US doctors. It's a cultural difference in the practice of medicine. Of course, it's also prevented things like the Thalidomide tragedy that struck Europe, while its use was refused by the FDA pending more testing (although that testing meant that there were still people in the US who suffered).
On the other hand, it is likely that there are people in Europe whose lives were saved by treatments that a panel of US doctors nixed because it was deemed too experimental, and they went with older treatments. In the case of stem cell injections (at least as far as the state of the art is now), it's probably a mix of both: some people do well, others have all kinds of bizarre growths or cancers.
obMySource: My father worked for Scientific Products for many years, a (no longer existing?) company that made equipment for hospitals. There are two semi-retired doctors who serve/served as outside doctors for some ethics panels at local hospitals and are friends of the family. One practiced in Europe as well. They've all chatted about this topic during several holidays, and I find it interesting. Incidentally, they all think the current US system stinks and is getting worse, and the doctors practiced medicine all their lives.