12 year old parking ticket

Forget it. No one is dragging up a 12 year parking ticket. This classic, "Let sleeping dogs sleep." If you didn't pay it, it has not been paid. The administrative charge was by the rental company for turning over your name and address so that the ticket could be mail to you. Personally, I would ignore it. Way too old. You couldn't collect on a 12 year old ticket in the US.

According to this site: https://italianviaggio.com/italian-traffic-fines-a-complete-guide-to-fight-your-ticket/
you are well past the statute of limitations. So you can safely forget about it.

I am more surprised that the rental company charged you an administrative charge now. I would dispute it with my credit card. I’ve done so in the past for similar charges by the rental companies in Italy (but not for a ticket since I never got ticketed). I don’t know what those extra charges might have been for, but I disputed them with my credit card. The credit card issuer investigated the matter with the vendor (in both cases it was Europcar), but Europcar always failed to provide a response to my credit card issuer, and the charges were permanently reversed and didn’t have to pay. I’d do the same in your case.

I read that cc charge as being done 12 years ago
Way too late to reverse
Way too late to worry about the ticket as others have said

When I went through immigration in Rome last year, I did see your name on a wanted poster, so take care. Of course, by now your appearance has changed, and you have a different Passport Number, so I would go for it. If they catch you, a small bribe should get you out of any trouble.

But seriously, what you paid was simply an administrative fee for the rental car company to turn your information over to the police. You should have received a separate notice of violations (Sometimes a year or so later) from a third party notifying you of the ticket, where, when, etc.; then an amount to pay (you would have remembered, maybe a couple hundred euro) and how to pay.

If you say you never received anything, fine, after all this time they likely either decided it was not worth their effort, or it has been lost in the very efficient Italian bureaucracy, or you thought it was junk mail or a scam and pitched it. Go, have fun, no worries.

I am still not clear about what you wrote. Were you charged the admin fee by the rental agency 12 years later? If so I would dispute it with the credit card company. If your card was charged by the rental agency in 2010, then it’s ok. You were charged that fee to provide your information to the authority who issued the ticket. No the amount charged by the rental agency was not used to pay the ticket. You should have received the ticket separately from the Siena Municipal police. If you didn’t it is because some cities don’t bother to send those tickets to foreign residents because they rarely get collected.
Your name will not appear in any database, not even if you get pulled over by the Municipal Police in Siena. Let alone the Polizia di Frontiera. They have bigger fish to fry.