The important question here is: Who issued the parking ticket?
My guess is:
If it was not issued by a state-recognized police officer, traffic officer or other type of authorized law enforcement officer, it is not a legal ticket.
A legally-issued citation is only resolvable in a court of law or in an administrative proceeding authorized by the state or DMV. The process is NOT issue the ticket, collect the fine. In between those two steps is the step that says you have the right to fight it.
In NYC, they installed cameras at red lights to catch people running the lights. The cameras took blurry pictures car (never getting a photo of the driver and in most cases, not even a license plate) and the tickets were processed and mailed out by a legal-sounding entity which no one had ever heard of before. It turns out that it was a private company with no legal authority to do anything and the only tickets that were paid were the ones given to people too uninformed or too intimidated by the big red letters on the ticket saying "PAY THIS AMOUNT."
If the ticket was not issued by a state-recognized law enforcement officer, do not pay it. Send them a letter telling them that if they take any further steps (such as reporting it to the credit history companies) you'll take legal action against them.