That's not how it works. I had to fight a ticket from one of these once.
An invalid ticket, for the record. I was innocent and I could prove it with dash cam footage. I did not run the red light, but as usual everybody acts like accusation is the same as guilt and you know how that song and dance goes.
First, those cameras are almost never operated by the state or the police. They're run by a private company which is under some kind of contract with your state or municipality. You'll find this is why racking up tickets from red light cameras usually can't put points on your license.
Anyway, you will face your accuser in court if you challenge the ticket. That person will be some lackey from the company that owns the cameras, whose job it is to show up to court. Theoretically this person was also supposed to have reviewed the evidence related to the incident in question, and this is what lets them get around that pesky constitutional requirement you mentioned. In my state the requirement is that two pictures must be shown, a before and after, positively depicting the vehicle in question crossing into the intersection. In my case the second picture was mysteriously absent from the ticket, which of course the state still treated as "valid" until I challenged it. This despite the conspicuous empty square on the printout they mailed me where that photo was supposed to be. The twerp from the camera company tried several tactics (unsuccessfully) to weasel out of producing the second picture until the judge forced him to. To no one's surprise whatsoever, it showed my car exactly in the same spot as the first picture and my ticket was dismissed.
I still had to take a day off of work to contest it, though, and the private entity knowingly lied and attempted to slap me with a fraudulent ticket knowing full well they would never actually be punished for doing so. And they weren't.
The guy whose case was right after mine on the docket was disputing a similarly bogus ticket, which he showed me. He was a big black dude with a Harley I saw parked outside. The "damning" photo evidence printed on his ticket showed a skinny white guy in a wife beater on a crotch rocket. I have to imagine he won his case as well, but I did not stick around to find out.
So the system is indeed still bullshit, but not in the way people expect.