OP: Your biggest problem is that you haven't accepted the advice of the people in the thread. They went about giving it in a pretty shitty way but they gave you advice, nonetheless. Arguing with them is stupid because you asked for advice.
If you really think you don't deserve the insurance hike, then fine, go to court and try your odds. When I got my ticket I didn't care about the $90. If you do, fine, borrow it from the parents. But let's focus on the insurance. Think about it this way: the reason they hike insurance when you get into an accident is because statistically if you get into one accident, more are likely to happen. You've labelled yourself as a driver who is distracted. It doesn't matter how small the incident was. It happened, because of you. Therefore, in all "fairness" you probably should have an insurance increase. A better driver, not deserving of an insurance hike, wouldn't have rolled into the car in front of them.
Sorry man, but that's how it is. Like I said, try your chances if you want. I got lucky with my ticket, going about 20 over but in a state that didn't report it to my state's DMV, so my insurance never found out about it. They most certainly should have, though, but nonetheless I paid my ticket no questions asked. Live and learn, that's all you can really do.