I don't have the link handy for the Orange County Comptroller, but suggest that you use this link to confirm a rental reservation instead:
www.mydisneyreservation.com/DVC
You need the confirmation number, resort, check in date and the name of the primary guest on the reservation.
If the member doesn't own a WDW
DVC resort, they won't be on the Florida OC website. You would also need their exact name as titled on the contract to find it.
FWIW, I'd rather check to see the owner actually made a reservation in my name than go through all the trouble of navigating the FL OC website.