Socialism has a very broad meaning, encapsulating everything from far-left (communism) to center-left (social-democracy, what you call "fake" European style socialism), just as conservatism encompasses everything from fascism to moderate center-right politics. Deal with it. The word "communism" exists and has a more precise definition that fits your unilateral vision of socialism so use this word instead. It exists for a reason. Let "socialism" exist in all its richness and -yes- contradictions.
I'm from the UK and we have socialised healthcare. I understand that there is a lot of propaganda against this in the American media. Is that right? I don't understand why anyone would want anything else.
The NHS has its problems, but these are not due to its being socialised. They are other factors (often stemming from capitalist sources). We have private healthcare if people wish to use it, but most people don't.
If people from the UK talk online to people from the US and mention their support for a socialist healthcare system, they often get called "communist". It's quite surreal. America has socialised schooling, police service, fire service, libraries etc. Do they not recognise this? I get asked "Why should my taxes go to pay for someone else's healthcare?" … my answer is "Because the privileged looking after those in the most need is fundamental to a civilised society". Imagine if children born into poor families didn't call the fire service to rescue their baby sister from their burning house because they couldn't afford the fees or couldn't afford to call the police when they were being attacked. It's ridiculous.