Why is it possible to set traffic lights wrong?

It seems like a rather simple algorithm to check if the traffic lights on a given intersection is set in a wrong/dangerous/conflicting way. Why is it not done?

Long story: I had a traffic an ugly traffic accident the last Friday. The area is new, all the traffic light equipment was installed recently. I had a green left arrow, so I was turning left. Three cars in front of me in the same left turning lane, one behind me. So I am sure I had the green arrow and also I am sure it was there when I was entering the intersection. Suddenly, there was a car approaching me going straight from the opposite direction. There was no time to avoid, just hit brakes and pray.

The girl driving the other car told me she had a green light too, going straight. I could not believe. So, I went to the intersection yesterday and watched lights. I had seen it: straight in one direction and green left arrow in the opposite direction overlapping for almost a minute.

I called the police to report the traffic hazard.

They did not sound surprised at all. I am assuming that there is a lot of software involved in traffic light control nowadays. Obviously, there are three independent inadequacies: (1) software that allows programming traffic lights in a dangerous way, (2) software that controls traffic lights and (3) the person who did the setup. Why is it not done the right way?