Interesting perspective Rockdoc but the letter you received should have also at least confirmed the originality of your Parker. In general, All you're going to find out with a factory letter is the name of the dealer the firearm was shipped to as it was and still is rare for firearms to be ordered direct from the manufacturer. For example: Colt sold the bulk of their production to 7 large hardware stores and a typical letter from them will state yours was 1 of XX in a shipment to Simmons Hardware or Sears Roebuck on a certain date. Now what a find it would be if the sales invoices for some of these stores were to ever surface.
Jim