Of course. As has been mentioned, many of the very first cars had buggy tops that folded down. What I was referring to was Eztrete’s post about the Chevrolet “turret top” replacing the canvas covered, wood-frame tops of the 1930’s.
The part of the top that appears “different”, here,here, and here, is a cloth, usually duck or canvas, covered, wood frame set into the metal of the top as in these 1934 Chevrolets.