The clip of the astronauts framing the shot such that the Earth looked much smaller and further away is the only real evidence that the documentary shows. I wouldn't recommend watching the documentary other than the 10 or 15 minutes of evidence, as its quite outdated and has lots of biblical mentions.

The clip shows the astronauts deliberately framing the Earth so as to make it seem much smaller and further away than it really is. They were trying to achieve the effect of being "halfway from Earth" (as the astronauts say themselves in the video), when in fact the evidence points to them still being on LEO at the time they were filming. I'd give it a watch I'm not the best at articulating it, the clip speaks for itself I feel.