I first knew that I had some form of autism when I saw a news story on low-functioning autistic kids back when I was still in my early 20s. Their rocking and their dislike of being touched were immediately familiar to me. When the reporter asked the psychologist why the children rocked like that, the doc said "we really don't know that yet" (this was in the early 1980s, when very little was known about autism). I held up my hand in my living room, rocking in my chair and said aloud "Ask me, I know they why they do it. They do it because the world is too intense and it effing hurts." It was another 20+ years before I was officially diagnosed.
As for people assuming that a person is autistic because they rock, yes they do. I sway from side-to-side, constantly when I'm standing (and sometimes rock back and forth on my feet), I just can't help it - I can stop, but only for a brief moment, and it's for the same reason - I'm STRESSED, 24 hours a day, 7 days a week, 365. I live in a state of high anxiety, because of all the sensory overload and the fact that my brain can barely process it all fast enough for me to function. Over the years, many times people I was talking to at work would ask me if I could stop, because it made them dizzy to try and carry on a conversation with me and on several occasions they flat out asked me if I was autistic. They were usually joking, but when I answered "Yeah, I think so - lil' bit." I wasn't.
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"I don't mean to sound bitter, cynical or cruel - but I am, so that's how it comes out." - Bill Hicks