[size=12]I think that the cast iron parts were all tinned (coated with tin at time of manufacture) like the grinders that Griswold made, rather than painted or Jappanned. That would be the base, the presser plate, the strainer plate, the yoke, the handle, and the two Kremlin-shaped tops that the yoke fits around. The side rods themselves probably would have been steel, for strength. I don't know for certain, but I think that the only part that was painted battleship gray when that was the desired finish would have been the outer sleeve.
A lot of the presses don't have the logo on the sleeve. There should be a logo on the bottom of the base, but if you have it mounted on a board of some kind, or if it's very rusty, it may be hard to see.
As to rusting up top vs down low? It'll rust wherever somebody didn't wash it properly, or it'll rust wherever somebody knocked the finish off first. The top probably got battered somewhat for every ham-handed miss whilst attempting to center the presser plate into the sleeves. Maybe that's why it rusted first. But, I'm guessing...[/size]