I replaced my late '68 a year or so ago. The set up on the door when I removed it was as follows:
outer: Chrome molding and inner felt
inner: glass side inner felt, with rubber molding to door panel.
My Assembly Manual shows no rubber on either side only the felts, GM part numbers 394589-90 for the outer felt and part number 3937265-6 for the inner felt.
The page number in the manual is H149.
I don't believe that my car had ever had any previous restoration done in this area. I looked to see if I could find any remnants of rubber on the outer weather strip, but found none in the disassembly process, and the assembly was not loose like something was missing. I ascertained that it was original to the car. The car has been repainted once, and this area was masked off rather than removed prior to paint which was very evident when everything was disassembled.
When I ordered parts, (Riks) the inner assembly with the felt/ rubber came as one unit, the outer come separately. For the outer, I only needed the felt as my chrome molding piece was in good shape.
Hopefully this helps some... I never really got a good feel that anyone had one correct answer. I checked out the '68-'82 Corvette Restoration guide, while it discussed side windows It didn't say anything regarding the weatherstripping, either in the window or the door section. Some said the assembly came with rubber on both sides, I saw no evidence of this on my car, so I left it off on the outer side. To add to my confusion, I have seen it both ways, with and without outer rubber, on a '68, but you could tell that each one had had restoration.