So for the remastered project they should have used footage from the skylab-launch, that would have done nicely. But the iconic Apollo-Saturn combination with the red launch-escape rocket on top, indicating a manned launch, has always been terribly jarring. Leaving everything as it was is just cheap.
Is it worth pointing out that this footage of the Saturn with the launch escape system showing a manned launch was, in fact, Apollo 4, which was an unmanned launch?
Incidentally: Apollo 4 launched in late November 1967; this episode aired in late March 1968. This must have been among the first times that the Apollo 4 footage was ever used for pop cultural purposes; it's hard to imagine many making use of it before then.
Since there was only the one Saturn V launch to use the stock footage of the liftoff is free of mix-and-match glitches. However, there is footage on the ground that uses the Saturn 500-F Facilities Integration test article as well as that of the Apollo 4 rocket. The differences are clear in the roll markings of the first stage -- the 500-F has a horizontal band across the first stage, with long black stripes like tines of a fork going down, and on top of the third stage is a sort of checkerboard pattern of white and black spots. On the actual flight articles, the first stage has shorter vertical black bands with no horizontal stripe, and the third stage has a thinner vertical stripe.
(The 500-F was designed to have roughly the size and mass distribution of the actual rocket, so that handling facilities like the Mobile Launch Platform could be tested and debugged before actual rockets were available. In Stephen Baxter's exquisitely awful novel
Titan this is actually refurbished into a flight article, which is not the piece of the book that makes the least sense, but it tries to be.)
Saturn V stripes are a common problem in modelers and special effects people. Even the team that made
Apollo 13's special effects -- which did not use any stock footage -- got the first stage roll markings wrong.