Right, I was just talking about the intent part of assault. I wasn't talking about battery.

I'm not going to do a fifty state survey, but Florida defines "assault" as follows: An “assault” is an intentional, unlawful threat by word or act to do violence to the person of another, coupled with an apparent ability to do so, and doing some act which creates a well-founded fear in such other person that such violence is imminent.

Note how "doing some act" doesn't require intent.

Battery occurs (in Fla.) when a person: actually and intentionally touches or strikes another person against the will of the other; or 2. Intentionally causes bodily harm to another person.

So you're correct that battery requires intent.