You have obviously been injusticed, and I feel you should stand up for your principles, even if it means you losing the case. I think you should not give in to this gross injustice, and fight for your justice.
I'm not asking you to cause chaos and rebel, I just think you should do what any man with integrity and morals would do. If you lose the case, you'll have to face the consequences, and it probably won't be too fun for you. However, you will have a clean conscience and you can proudly say that you didn't do anything wrong.
If you pay the fine even when you clearly didn't do anything wrong, then you would have "sold out" and you'll be just as bad as the NEA officer (who ought to be a good, honest, government official) who lied that your drink can was empty.
Just my two cents worth, provided what you said in your first post was the truth. Heh.