Hertz have just updated their Gold terms, so I've taken a moment to review this.
The general rule across all Europe is:
" Unless stated below or in the Country Specific Terms or with the prior written consent of Hertz, Cars may only be taken into the following countries:
Andorra, Austria, Belgium, Denmark, Finland, France, Germany, Gibraltar, Italy (but see paragraph 5(g)), Liechtenstein, Luxembourg, Monaco, Netherlands, Norway, Portugal, Republic of Ireland, San Marino, Spain (not including the Spanish Enclaves of Ceuta and Melilla), Sweden, Switzerland and the United Kingdom (including Northern Ireland)."
The specific 5g rule is
"Mercedes, Porsche, BMW or other prestige cars and convertibles of any make must not be taken into Italy"
I would suspect that they'd call an Audi A6 a prestige vehicle, so would not be allowed into Italy
The specific rules for Germany adds on permission to go into certain additional countries (former eastern block), but the Italy prestige restriction still applies.

The only way I can see that you can make this work with a Hertz premium car is to actually start the rental in Italy. Though as others have said, in Italy you want the smallest vehicle that you can fit in. I was upgraded to a Mondeo (Fusion in N America) on my last Italian rental and it was a nightmare in crowded streets and narrow parking bays.