What you (OP) need to do is file for disclosure. The police officer really doesnt have much on you. His/her entire disclosure will be explaining what the other party told him/her.
If you go to court, the only real way to uphold the ticket is if the other party shows up to court. Or at the very least, they have a sworn statement given to the cop. If you’re not a native English speaker, do also ask for a translator... so if the translator doesn’t show up, you would also have a good chance of these proceedings getting stayed.