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davidcyclebackThe good news is that Sy Seidman was a NYC news photographer when Mathewson was playing, and, since most people have never heard of Seidman, it would seem unlikely anyone is faking his name on the back of photos. The average baseball photo forger would describe his creation as a 'Bain' or a 'Conlon,' not a 'Seidman.'
Old gelatin silver photos, like with an original 1910s Ty Cobb or Mathewson, have a thin coating of gelatin on the front, used to hold the photochemicals to the paper. The gelatin is transparent and usually shiney. It's possible that the gelatin is what you describe as a plastic coating. Collectors of lower grade T200 Fatimas (gelatin silver photos) sometimes notice the gelatin when the card has a tear or worn edge.
Attractive original Christy Mathewson photos by professional photographers like Seidman are scarce and highly desirable in the hobby. If your is original, and naturally we all hope it is, you have a nice item.