I would not have paid the fine. It's one thing to contest a ticket where there's a dispute between you & the citing officer, but if you were not even stopped and cited, you should have moved forward with written documentation to the head of the reporting agency and contest the ticket in the court. Paying the ticket is basically admitting guilt.
I would imagine there's some pretty viable proof to back your story up. Video evidence, photos, cell phone records where you were, testimony from people you were with, etc etc. Why did you pay it?