We have visited Italy four times, each time renting apartments directly from the owner, or from an agency, for a week or more. We have had great experiences, with only one apartment, in Venice, not being up to our standards, although it was adequate and the location was great. It was handled by an agency and we did not deal with the owner..
Most rentals it seems are pretty much a business for the owners, that is, they do not live there, so I wouldn't expect to get a discount. We have found places via VRBO but not AirBnB, so I cannot speak to the latter. We have rented in Venice 4 times, and are returning this year to a great apartment in Dorsoduro that we rented two years ago. We have rented in Montepulciano, Greve in Chianti, and Vernazza, and will soon be going to Orvieto and Rome, where we have found apartments also rented by the owners. It is a wonderful way to stay in Italy, more economical, and it gives you more pace and the option to cook some meals, stay outside the main tourist areas, and make your own coffee, etc. We wouldn't travel any other way. Good luck.