I work in insurance claims and I think I can help you fight this from a perspective of, avoiding avoidable damage to your vehicle.
You see the stop if it is safe to do so can be broken into a couple of pieces as there are a few factors to take into consideration:
1. Experience of the driver (this includes with the vehicle you are driving and how long you have been driving)
I mean if you have only had your car for a few months then driving in the rain, cornering etc aren't exactly your best points yet
2. Distance from car to line when the light went yellow.
If the distance was <3 seconds to the line then legally, just like with following Third Party vehicle, you don't have enough space to safely stop.
3. Reaction speed of the driver and when they noticed the yellow light.
Most people cruise towards lights and don't expect certain intersections to go yellow as they approach due to experience with that intersection and this also depends on what they are doing in the car. Generally the 3 second rule applies here to.
4. If you had a Third Party behind you.
Police oft forget if you have a hot car with an expensive paint job, insurance won't always cover the full cost of repairs and in many insurance company cases, the vehicle is worth less to write off than to have resprayed and repaired. This means if there is someone right up your arse and you are having to brake suddenly they would not have the chance to stop and will likely cause damage to your vehicle, putting you in a nasty situation. Also if it was the police right behind you then you can put that under entrapment as if they were right behind you they are effectively trying to bully you forward.
Think about these points and what others have said, the only fines I have ever recieved are parking fines and my last speeding ticket was for 70 in a 60 zone when both myself and the officers knew I was doing over 100 but as they had no gun and no clear sight of me they could not enforce what speed they knew I was doing!