That’s not exactly right. You are eligible, you just need to do something to get it. Ie if you register as unemployed, you will get insurance. Same with university students.
I don't think it's fair to say that Europeans started. Danes always bought US hardware over European arms, went to war when US called and lost soldiers. Now they are threatened with imperial invasion and called a 'bad ally' by their 'ally'. This was one of the most pro-US countries in the world.
Denmark is in NATO, US base is already in Greenland and I'm sure Danes would be open to add few more. There is no need to invade it. The moment it happens, Europe is lost to the US as an ally and NATO is gone.
Russia has been involved in sabotage, shooting down planes with Europeans (MH17), killing people they don't like in EU/UK for years now. If anything EU is extremely timid and does not retaliate.
Some of us live close enough that it's not really an option, surrendering to Russians don't work that great if you live in Eastern Europe. I will volunteer first day to join Polish Army.