That's quite a bit. It's one reason why people generally recommend train travel as less stressful, with cars mainly needed when touring rural areas in Piedmont or Tuscany, etc. Even then, if winery tastings are on the menu it is better to hire a driver.
They have a year to ticket you. I've known people who have come back from Italy and almost a year later got hit with 5-6 tickets for several hundred euros each. There doesn't have to be a policeman there. They can catch speeding and other infractions on camera and by law can nail you up to one year later.
It doesn't matter whether or not you ever plan to return to Italy. Italy has partnered with a very aggressive USA collection agency and they will go after you. And it doesn't matter if you rented from Hertz on a credit card you no longer have. They can make Hertz charge you on that canceled card, then Hertz will come after you.
As Forest Bump said, this has nothing to do with ripping off tourists. Traffic rules are different there. Just see what would happen to you (and your car) if you ever got a DUI over there, and they don't use 0.08.
I feel sympathy because this was a misunderstanding on your part. All I can say is that in a foreign country don't take translations for granted. The letter probably had mistakes. You see it all the time. Not to make light of it, but see here:
http://www.thelocal.it/galleries/cul...tions-in-italy.
When in Italy, waiters, hotel staff, and others start speaking English and we often assume they are bilingual. Not the case at all. They usually know ten sentences, like how to tell you where the bathroom is, etc. there are a lot of nuances, even when reading official forms. Same with newspaper articles. They're sometimes not understandable in a literal sense. This was probably a misunderstanding, but I don't think you should just ignore it and file a letter of appeal or explanation as it may cost you even more in the future.
When you are late on a fine it usually automatically doubles. The proper way is usually to pay, then appeal. Even then in Italy, for certain fines you have a right to appeal but if you lose, they'll increase your fine quite a bit for wasting their time with the appeal.
Would you mind sharing more about the type of fine, infraction, where it happened, and other details as it may help others provide you with some options.
When in doubt, take a train.