My 2 cents worth (and you can get change from that
). If the serialization books says it was made befor the game of skeet was even invented thats a big red flag to it being a true skeet gun. I once had a vent rib DHE 12 that was stamped skeet in/skeet out but it was not an original skeet gun
The checkering isn't correct on the forarm. The only letter that matters would be from the PGCA. Skeet guns can bring a premium dollar and IMHO this isn't an original skeet gun. All the true skeet guns I have seen were mfg after the Parker Gun Co was sold to Remington. If the receiver says PArker Bros than (once again my opinion) it's not a true skeet gun.
At the end of the day remember this "it is much easier to buy a gun than to sell a gun".