I used Avis in Italy many times, and don't remember that it ever were possible to get the car without a credit card. Actually, it's in their FAQ:
https://faq.avisautonoleggio.it/Res-Channeling/Reservation-E...
In short, the translation is: prepaid cards (and only certain types, not Electron/Cirrus/etc) can be used to pay online only, and another card among those accepted (i.e. a credit card) should be presented at the desk.
The UK version of the FAQ tells basically the same:
https://faq.avis.co.uk/1492093922
"PREPAID cards are accepted online however they are not accepted at the counter which means a non-PREPAID card must be shown at the rental station (together with the PREPAID card)"