In Pittsburgh the yards look at you strangely when you try to get your shixt back. I think most people just don't even try.
I've had two vehicles towed for lack of current registration. Both times they were car projects that tested the limits of other people's patience by sitting around monopolizing a parking space (parking spaces here are defended with chairs and stakes and cones and gallons of off-yellow paint that fool out-of-towners and meter-maids alike).
The first time, I actually needed my car back, so I wandered off to the yard and surprised the owner by asking him to return that which he had taken. He was too shocked to rip me off for more than a few extra days of storage fees.
The second time I just did what everyone else in Pittsburgh does with towing companies, and sent them the title to the car. It's like magic, one minute you've got a huge impound lot bill and a citation, and the next it's all smiles and forgetting-this-ever-happened.
So Round, you're 2000 miles away, but I bet the tow yards work pretty much the same way. Possession is nine-tenths of the law (and apparently not a crime there, weird); the yard now has that nine-tenths locked up tight, and the cops probably brought them the other ten percent when they brought in a 5am drunkped and removed its plates.
Beat, the stories and worlds we inhabit.