I think the photo is a 65 Chevelle. The Galaxy is the car that is for sale.
I agree with you—that is a GM body, not a Ford Galaxie.
The flat dual headlight grille in the front and the square rear taillights make the 1965 Chevelle the best candidate.
The Galaxie 500 had a severe roof angle in the rear and large round tailights, and a rear with rounded edges.
Aside from that, the article was news to me as well. I remember the Chrysler Turbo cars from 1962 or so that were going to revolutionize automobiles.