If this watch on Amazon (or any other website) is a "new" watch, it likely is not being offered by an Authorized Dealer, as internet sale of Rolex products by their dealers is expressly prohibited. Prohibited to the point that one such sale will cause immediate revocation of their "authorized dealer" status. As such, Rolex products purchased online ARE NEVER eligible for a factory Rolex warranty, even if it is a new watch. The only way the warranty could be registered from an online sale would involve fraud and violation of Rolex's dealer policies, thus implicating the purchaser and seller in a crime. Rolex is EXTREMELY protective of their product, pricing and dealers and has a zero tolerance policy for their dealers who do not comply--just ask some of the 20+ jewelry stores in Florida that were axed in the last 2 years or so.
Fakes are becoming more and more common, and harder to detect by those other than a jeweler who knows Rolex products. When all is said and done, there IS risk associated with buying a watch online advertised as Rolex. If you want to be assurred of the "genuine article" with a Rolex warranty, you must buy through an authorized dealer.