Back when you used to get a whole new plate each year, with a new number, the police came to our house one March when my mother was in the middle of making Hamantaschen, looking for my father, the only adult male associated with a license plate that was on the car that had been stopped several hours earlier, and the driver had gotten out and punched the officer, then driven away. If you know that my father was short, wore glasses, was at the time pretty then, and very professorial in polished shoes and suits-- well, anyway, my mother showed them that Dodge Dart in the driveway, and it wasn’t the make and model they were looking for, but the plate was right.
Turned out that people who are willing to punch out cops at traffic stops are also not good about getting their plates renewed.
Anyway, they have heard it all. I once got a parking ticket because, and I am not making this up, the city installed a meter while I was parked there. Now, I was parked there for three days, and I probably should have checked on my car, but at any rate, I never thought that excuse would fly. It did, though, because they were able to look up whether or not there were new meters installed in the area where I was parked.
You may not even need proof-- just say you don’t live there, and wasn’t visiting on that day, or any other day. Send them a photocopy of your registration with your plate number, and address. Tell them it’s your real address. If you live in a no, or lenient inspections state, and the violation was in a strict inspections state, it may be a result of their cracking down on bogus registrations, which I can tell you happens, because my mother, without telling me, registered her car at my Indiana address for three years to get out of inspections.
I predict this will be easier than you think.