I'm not from US but I believe this is incorrect. Everytime I visit there, I am always amazed to see how caring the people are. This is a sample size of one though.
It's uneven. There are many who are kind just like you say. But if you have ever seen the savagery in the comments on any HN-linked story on homelessness, that perspective is also well-represented in the US.
I think when people travel they generally visit the pretty and happy places. Surely people with mental health issues hide those issues while the person is there in order to fit in: else the person wouldn't fit in and would be ostracized and removed. See also anti-homeless laws.
Mental illness is absolutely seen as a weakness. You just need to hear how people gossip in quiet about someone who’s having mental health issues. Statements about people needing to “man up” or it being “their time of the month” are far from uncommon.
Growing up, my parents would make fun of my aunt for taking anti-depressants behind her back in front of my sister and I. When I was a kid, I didn't think much of it. Now being older and having gone through some dark times of my own, I am truly sickened by the fact that they see her in this "weakness" light. Imagine all the kids who faced the same thing but never saw the other side and wound up feeling the same way their parents did? My parents taught me a lot of great things but I am glad this was not one of them.
Individuals, sure. But the system? You couldn’t be more mistaken. Your health insurance comes through your employer. When you get sick or depressed, and you start missing work as a result, guess what happens?