And if it's your car, and you want to claim that it's not you, they ask you who it is.

In California at least, you can just ignore that question.

Not in many other states. MO for example specifically puts the onus of who is operating your motor vehicle on you, the owner. Or you need to declare it stolen.

But can they assign the ticket to you personally? In my experience, places that put the responsibility strictly on the owner of the car do so by removing the attachment to an individual's driving record and instead attaching the ticket to the car itself, like a parking ticket.

All automated tickets in mo are non-moving violations. So yes you are correct on "points". But mo also allows you to convert almost any driving ticket to a noisy muffler by paying 3x or more the price by paying a lawyer. Unfortunately even DUI (up to a point). It basically encodes the realization that the state just wants the revenue. Randomly assessed taxes on correct road use.

You can always directly fight the ticket too. I can't tell how far it is from legal graft... But I did avail myself of it, it would be dumb not to as the 3x cost for a ticket was still 1/2 what you'd get dinged by the insurance for the original ticket.