Yes, no question in my mind that this car started out as a Rambler American, not a Nash Rambler . . . although the American was, in fact, nothing more than the old 1955 Nash Rambler body dies being dusted off and pressed into service (now there's a pun for you!) to produce a "new" 1958 model. Although I don't think anybody was fooled as to what this car actually was, the 1958-1960 Rambler American was actually quite popular and did good things for AMC's bottom line during the Eisenhower Recession that affected nearly every other US auto manufacturer. It also beat the Big 3's 1960 compact Falcon, Corvair and Valiant to market by quite a bit.
I sincerely doubt that Mitt Romney's father George (President of AMC 1954-1962) could ever have envisioned a Rambler American looking like the puzzle car!