Does anyone know what the song is at 35:00? It only lasts for a few seconds. The credits at the end are too blurry to make out and googling the documentary and going on the history channel website hasn't helped.
The credits at the end are not too blurry to make out a music credit to "Big Yellow Duck". Their own website has a link with details about the program http://bigyellowduck.com/work.php?uid=AE40A7&category=Long%20Format where the sole music credit is to Stuart Kollmorgen. The fragment you mention sounds: upbeat, late 60s-style, guitar-based, and the riff sounds like something you know but just can't remember. You could contact Stuart Kollmorgen or Big Yellow Duck to get more information. Basing this answer on the publicly available stuff, chances are that Stuart Kollmorgen wrote a load of music in different styles to fit the content of the program. Done that way, I guess it's less bother with royalties etc than using original recordings, but maybe others with more knowledge can comment on how they do things in the world of TV music production.