For everyone's edification...I looked around at COMC and immediately ran into a ton of cards that had the same (read as "similar") back stains as my Gibson, so I'll display a few of them here:
fleer1.jpg
fleer2.jpg
It's pretty clear something was definitely going on inside of the 1963 Fleer packs. If Brian's recollections are correct and the cards were protected from the cookie, my guess is maybe at some point -- at the beginning of the run or later in the run -- the set-up changed and these safeguards were either added or discarded. (In other words, perhaps when the cards were first released there were no protective measures in place, but then consumers started complaining about the stains and Fleer acted on it? Who knows.) The high rate of occurrence of these stains seems to indicate that the dark brown/white protective cards were completely removed and it wasn't just a case of them accidentally NOT being inserted during the packing process from time to time.