Just as an aside to others who may be reading this thread...
DVC/Disney is being sure to take themselves out of the rental process. They never wanted to be part of it and the more interaction they have with non-members the more a case might be made that they condone/assist the practice. It's not Disney's responsibility to guarantee your transaction with a private individual.
I know it's scary and it's nice that you still have the option of calling the resort directly to see if it's in your name. However, that really doesn't mean anything more than that a reservation was made for you at that time. The owner can always cancel. Dealing with a DVC member to use their reservation is no different than renting a ski house or summer camp from an individual. In those cases, there is no one to call and verify. You just have to depend on the written agreement that you have with the person.
I'm surprised at the number of posters I've seen lately who have forgotten the name of who they have rented from or don't have the e-mail etc. You are spending your own money and need to take the time to be sure you've got a proper transaction set up. You should also establish that the person is renting you their personally owned points. Some people have begun businesses where they gather points from multiple members and then run a rental business. DVC has stated that they are going to begin taking steps to bring these businesses to a halt. It would be prudent to try and avoid renting from these type of set-ups.
People should also remember that renting is not the only way to stay at DVC resorts. You can always book directly with Disney just like you book other hotels. Generally, it will cost more but if you are staying over a weekend and/or get a discount the difference may not be all that substantial and provides you with the security of dealing with Disney.