Question regarding Chords

In Hook Theory I is written, that as long as the lowest note is a 1 it is a I chord. But e.g in this example in Hook2 1.3 Twist &. shout the lowest note on the IV Chord is a 6. So why isn’t this a vi Chord?

Or is the chord determined by the non shown part of the images. E.g. the images show a melody (right piano hand) and the chord is determined by the bass (left hand).