Mr. Rogers was my actual neighbor in Pittsburgh in 1999-2000, while I was at CMU. He would really go out of his way to have social interactions. He would always say hello and ask how you were doing in a way that felt like he actually genuinely wanted to know the answer. Case of the person in real life being exactly like what he seems like on TV.
This is one thing that always got me about the United States: people will ask you how you are doing, but they don't actually mean it, it's just a required pre-amble, a bit like the tones a modem uses to sync up with the other end. If he did it in a way that he actually genuinely wanted to know the answer that alone would set him apart in a very distinctive way. Most people really don't want to know the answer, but th…
Yes, we use it like "hello" -- but not always. Sometimes we mean it.
Since this use of "How are you?" trips up people from other nations so much, I've tried to be more aware of this. My compromise is that when I mean it as a greeting rather than a query, I'll say "Howzitgoing" like a single word. If I mean it as a query, I'll look the person in the eye and ask "How are you doing?"