Correct. The tail lamp and brake/turn lamp filaments are grounded through the reflector assembly to the body via the screws. Only the reverse lamp has it's own independent ground with a wire to the body. This is because the reverse lamps were an afterthought and were added some time later in the '66 model year. You can even see that the backup lamp reflector is a separate piece that's riveted to the main reflector and insulated from it by a paper(?) gasket.
Hence the separate ground wire.
The main lamp housings/reflectors are also insulated by plastic squares so that the two metals don't actually touch. Only the screws create the interface for grounding.
If yours are very rusty and loose, this could cause trouble. If the housings have been painted, or the body was painted inside the screw holes, this could cause a problem.
Also if your main body ground was removed and never replaced during a battery cable change, this could be part of the problem at the very least. Not to mention that the bodies themselves get rusty where the panels were spot welded together at the factory. When they were new, no problem passing electrons from one panel to the other. After 50 years of rust and paint, it's not always so cut & dry.
So always check, fix, add and upgrade your vehicle grounds.
Paul