I don't know the show, but when I first watched this clip (under the title of "greatest shot on television") I totally bought in to the hype and thought it really was amazing. You start out just walking alongside him, and only slowly realize where you are and what is about to happen, and everything is perfectly timed and composed: he ends his walk, reaches the conclusion of his explanation, and you realize what is going on, all at the exact time the launch begins. Brilliant!
Except that this is not "a shot" at all. I just hadn't noticed on my first watch that there's a very obvious cut just at the end of the "walk". It's a different angle from a different location at a different time of day, and he just has one sentence to say before he looks back at the blast off.
It would be no different from any news reporter on location at the time, reading a prepared message ahead of the launch, timed to end before the launch itself with no need for extensive rehearsals, the launch timing is widely broadcast, you time yourself accordingly with your talking speed, by adding pauses, etc. And on top of everything they probably had to do it live too.
I have no issue with James Burke or his show. And this scene is really beautifully done. But it's not the greatest shot in television. It's not even one shot!
(edited: typos)