I looked at Triumph TR6 1969-1976, Brookland Books. It's a compilation of road tests from all the magazines of the day.
I did not see any caps mounted at angles or with the hinge to the rear. I did see them open from the drivers side, passenger side and rear to front. Rear to front was from a 1969 article.
These would all be cars that went directly from the dealer to the media. I can't imagine they were altered in any way.
From this, it looks like you can take your pick.