Is your car a '67? I would have to guess someone replaced the base at some point. Since they used the flip open gas cap for several years you probably got one of those. The base and flip part are two separate part numbers, IIRC.
No, the flip part of the cap was the same, 67-70. The base changed, as the contour of the taillight panel changed, and there were about 4 different emblems, but the only unique flip cap was the 69 GT, which had a gear-tooth motif, while the 67-70 had a smooth groove. The 67-68 Shelby had the Mustang cap, but instead of the Mustang emblem, it had a disc medallion.