To buy a car in Italy, I don't think you have to be resident there. But to register your car in Italy, you probably have to be resident.

And yes, "resident" means that you pay income tax on whatever income is allowing you to reside in Italy - where that income comes from is not important, it's where you reside while you're making it. What's worse is that if you're resident, you're also expected to pay Italian social insurances on your income so that you're eligible for whatever health care, retirement and whatever other social services they have there.

Depending on what country you are coming from, there are usually tax treaties or special provisions to make sure you don't get double-taxed on your income from elsewhere. But it's one of those facts of life that you wind up having to pay your taxes someplace. (Usually - there are a few tax havens left in this world, but not many.)
Cheers,
Bev