They're a very "proud of their freedom" aka being arrogantly pompous to the point of idiocy - as we are now witnessing, if them voting Trump in wasn't evidence enough.
First, Hillary actually got more votes than Trump. It's the crazy Electoral College system that handed the presidency to Trump. Yes, they are proud of their freedom; there are historical reasons for this, going as far back as the motivations of the first pilgrims emigrated there.
It's a vast country, and the cultural, religious and political variations are immense. Some of the pomposity and idiocy is based on misinformation and not knowing any different. Many parts of the US are very closed off and parochial - and that includes the news media, which are VERY focused on local news. Historically, the various churches have been the foundation for social interactions. And the vast majority of Americans never travel outside the US, have no idea what socialized medicine is actually like, and assume that countries with monarchies are not democracies
However, when you encounter Americans in San Francisco, New York City, Chicago, et cetera, they'll often start apologising about Trump as soon as they realise you're European...