"That sounds exactly like an urban myth along the same lines as 'seatbelts kill more people than they save'. Has it ever been proved?"
I hope you will look further into this - you may be interested to learn (I was) that a nearly perfect intervention for red lights being "run" is to lengthen the yellow signal.
It costs nothing and works as well, or better, than red light cameras - and with none of the artificial, unexpected driving behaviors that can cause rear-end accidents.
Yellows have been shortened on purpose to raise revenues from tickets. If cities cared about accidents and congestion, we'd have less lights and more traffic circles, but that means less tickets and more thought and effort than lowering the yellow light time.