They are not. YOU are responsible for tour health insurance, just as you are responsible for your homeowners, auto, and life insurance. Many employers choose to offer you health insurance as an additional benefit to your total compensation package, but until Obamacare, there was never any requirement for anyone to have health insurance as a stipulation on employment. Employers choose to offer this benefit for several reasons, as it is a net savings to them, versus directly compensating the employees.
Are you assuming your employer will fire you if you get sick? There are laws protecting you from that, at least in my state. Also, if for some reason you choose not to go back to work during an illness, programs like COBRA allow you to remain on the employers group policy, at their group policy rate, out of your own pocket.
I think that is part familiarity, and part the news you watch. Many Americans are terrified of gov’t run healthcare, likely for the same two reasons. By a similar token, I’ve met many Europeans who think they have a 50/50% chance of being shot by us “gun-toting” Americans, on any given trip to the US.