In this country, you are automatically guilty of LOTS of things just like this. Your car is given a parking ticket. You may not have parked it in the illegal spot, but guess what? As the owner? You're responsible. Your car is parked in a handicapped spot. You may not have parked it in that spot, but guess what? As the owner? You're responsible.
Edit: If your car was left in gear and is EMPTY, rolls down a hill into someone's car or a little kid, guess who's responsible? You. As the owner of the car.
Your car is ticketed for entering the intersection after the light changes to red. Even if your car is still in the intersection after the light turns red, no photograph (or video) will be taken and no ticket will be issued. At legal right-turn intersections, the camera will only take a photograph (or video) of your car if you fail to stop before turning.
A photograph of the violation is mailed to the car owner. Usually, a video or additional stills are available on line.
In some states, if you aren't the driver of the car, you have to appear in court to establish "by photo comparison" that it wasn't you. Not in all, because it's a civil violation, not a moving one.
I have absolutely no sympathy for people who run red lights. They kill people every day.