I cannot access the video (in work) but from reading the post, it sounds like the mistake you are making is to consider the role of the chord to be necessarily defined by the bass note you are hearing. Whilst that is normally true, there are occasions when the bass note is changed to re-orientate the voicing. Most slash chords are actually a major, minor or dominant with the third or fifth in the bass. The chords that are used are defined not by the root notes but by the way in which they are used. The same three notes that make a voicing can be any number of chords depending on how they are used as opposed to what chord they 'spell'.
For example; CEG is a major triad in a C chord. They are, however, also the 3rd, 5th and 7th of a Am7 chord, or the 5th, 7th and 9th of an F# half diminished and so on. The chord will be defined not by the notes alone but by the chord before it and the one after. I suspect, but cannot be sure, that your bass notes in the Air tunes are not root movement and so your chords are skewed. Often, the actual movement is simpler than you think and probably amounts to a diatonic sequence redefined by some unusual note choices in the bass.