The term "rare" is relative, but the seller is right about the production numbers in 1961 and the serial number does confirm it's a '61. $1300 is serious money, especially when you consider how much more the buyer will have to spend on NOS Campy components to make it rideable with the period correct group. The fork rake, chainstay length, and eyelets would seem to indicate it's a P11 "Tourist", not a P12 "Road Racer".

The Waterford website has some interesting pages devoted to Schwinn Paramount history.

The Paramount pictured on page 2 of the 1961 catalog (courtesy of Eric Amlie and Bob Hufford) has the seat tube decal; the eBay bike doesn't. Since the seat tube shows chrome where the decal should be, repechage is probably right about it being a chrome plated frame.