ticket issued based on judgement call

I was at an accident at an intersection where I was turning left while going north, and a car coming from the south hit me. I had a green arrow, but the other driver claims they had a green light, and at the time there were no witnesses. The police officer ended up citing me for 'failure to yield when turning left', because there was no way to prove which of us was telling the truth.

Incidentally, the other people actually drove about 200 yards away and called the accident in from there, before coming back to the scene of the accident.

Is it normal for a police officer to use a law that doesn't apply, when one of the parties is lying, in order to assign a ticket, and what is my recourse for fighting this ticket?

Thank you very much.