My question regards a moving violation in the state of: Florida

I was involved in an accident while backing out of a spot in a supermarket parking lot. There was no damage to my car and significant damage to the other car. The other driver called her insurance, but did not want to call the police. Believing I had a strong case that it was her fault, I called and we waited for an officer to show up. When he did, he cited me for a $150 moving violation, "improper backing." His only reasoning despite the other driver saying she saw me slowly backing out and "tried to squeeze around me" was that "9/10 or 10/10 collisions involving backing out find fault with the driver doing the reversing." Now apparently it will be found that I am 100% at fault.

My question is simply: Does this officer have the ability to write a moving violation in a parking lot? I have heard that since parking lots are private property police can file reports, but not give citations. I am wondering in case I show up in court to try to plead my case for the ticket.