Am a lawyer - You're correct. Intent is key and almost all laws are based around intent or, in legal parlance, "Mens rea" or the guilty mind. That is what separates a legal act from an illegal act: the intention behind it.

Suppose you are leaving a store and heading to your car. For whatever reason, the button on your keys unlocks someone else's car that is the exact same make and model as yours. You hop into the car, your key starts the ignition, and you drive off (Yes, this has really happened). That isn't legally theft because you legitimately believed that was your car - aka you didn't intend to take something that wasn't yours.

For 98% of laws, in order to be convicted, the government needs to prove you intended to commit the crime. Obviously, I'm oversimplifying what is a very complicated topic you spent two years learning, but that's the gist