Borders between states are hardly the same as borders between countries, and Portugal is not representative of Europe. Europe is a region with multiple cultures, languages, countries, and governments.
Well that's the point that he/she is trying to make isn't it? States in the US are more like to countries within the EU. That's in part why I think a lot of people from the US refer to 'Europe' as a cohesive entity, because in many ways it is. Different states and different countries are at different levels of progress.
States in the US =/= Countries within the EU. Europe is really not a cohesive entity. Different languages, different history (stretching back a thousand+ years), completely different value systems, cultures, etc.
Trying to insinuate that the degree of differentiation between states is the same as between Europe countries is utter absurdity. Clearly, trying to track healthcare across different governments with different languages and different cultures is much harder than trying to track healthcare across different states with the same language, the same national government, and a very similar culture.
Culture and that other stuff you mention are important, but so is size and distance. In the same way that someone who moved from Austria to Scotland would be tolerant of differences in official services, so is someone who moves from Seattle to Orlando.