I'm not familiar with Italian law, but it's maybe possible the hire company will pay the fine and off-charge you. Italy parking and traffic offences are all still under criminal law, I think.
In the UK, the Penalty Charge Notice regime makes the owner of the vehicle responsible, so with hire and lease companies, a lot of them just pay the the PCN and off-charge the hirer/lessee, plus an 'admin' charge, needless to say !
