The sad thing about this is that police apparently lie far too often IF the above posts are to be believed. And they whine that we have no respect for them.
The best thing you can do is write the court (judge), the chief of police, the mayor, the newspaper and police organizations. Ask for an explanation from each and also ask that the policeman's record be annotated to show that you believe he lied.
This will cause them much more trouble than the ticket was worth. Maybe AAA would be interested in seeing if the public should be alerted that there is something funny going on in this jurisdiction with traffic tickets.