There was a period in the late 50s - early 60s that Randall or Textron owned Wagner and Made in USA was not yet inscribed into the patterns. This griddle was also sold unmarked as a Griswold #138, made by "Griswold Mfg. Co. Sidney, Ohio" (no Made In USA, either). In all likelihood, your griddle production was done in Cincinnati, thus the no "Sidney -O-".
Always bear in mind that counterfeiters were largely opportunistic, reproducing small, high value items. And recasts are typically just someone trying to make a usable piece, not a perfect replica.