Simon

Anders does play all 6 strings when initially showing the upstrokes.

Easier than asking a beginner to miss strings in a playing a chord.

He does explain later that chords may be played only using some of the strings.

Only 3 low, 3 mid strings, 3 high strings. 

All for differing sounds

This also applies to upstrokes where he explains it's normal to only play 3 or 4 of the high strings in an upstroke and not to worry about playing all the 6 strings.

It's a stepping stones approach

Dave