Having encountered a similar situation in Florence, we were disappointed but unsurprised to be presented with a contract of tenancy to sign upon our arrival at Lorenzo's apartment. As had been the case in Florence, no mention was made of this contract in Lorenzo's listing and the contract was not provided for reading and signing prior making payment through Airbnb. Knowing from experience that we would not be allowed to stay in the apartment without signing the contract, I was obliged to sign.
For your own peace of mind, I suggest that you request a copy of the contract from Lorenzo prior to booking and that the contract is signed by both parties prior to making payment through Airbnb (the contract itself states that "payment is made in advance for the whole rental period upon conclusion of the Contract").
Putting aside the issues with the check-in process, Lorenzo's apartment was a great place to stay in Rome. It is close to Termini and the Colosseum, and around 15 to 20 minutes walk to other key sights (such as the Forum, Trevi Fountain, the Pantheon and Piazza Novona). To get to Vatican City, we walked to Termini and took the Metro directly (but you can also go to the Cavour station just a few minutes walk away and change at Termini). There are plenty of restaurants and bars nearby and we took a break from a steady diet of Italian fare at a great Indian restaurant (Maharajah) located just a few metres down the road. The apartment itself is spacious and clean, with a pleasant, sparse minimalism in furnishing and decor. Lorenzo had set it up with a few essentials (including milk in the fridge - relatively rare in our experience) as well as a bunch of treats to help us settle in. The bed was very comfortable and the Wifi connection was great!