This 1964 penny appears to be double stamped on one side and not on…

It's nothing if not creative. It's probably a coin with one side worn off that had a second one pounded into it. Doubling leads to two images of the same side, not opposite sides coinciding. Look closely: is the memorial the same as on other cents, or inverted horizontally? Are the raised features the same as on other cents, or opposite (i.e., if a column is raised on a regular cent, is it raised on yours or a depression?). An inversion would suggest the banging of two coins together; a coin struck with a proper die will not be reversed.