"He is just "Strumming", not playing the instrument."

Who said "strumming" is not "playing"? Did Lonnie Donegan not "play" guitar? This assumes that there is one 'correct' way of playing the instrument - which, given the variety of styles in some of the examples mentioned above, is clearly untrue. Whether or not you like Sir P's song, he has chosen to use the mandolin to give a different texture from that which would be provided by a guitar or, for that matter, a ukelele. McGuinness - Flint did something very similar years ago on When I'm Dead and Gone, and on the "Songlinks" CD Tim Eriksen accompanies Still Growing with a very basic strum on "a cheap mandolin with a strip of paper woven between the strings" - and very effective it is too. Song accompaniment is not the same as virtuoso musicianship.

Incidentally Paul sounds to be playing his 'D' chord with a G drone at the bottom of it, which is a more interesting sound than just playing the chords from the manual. And if I'm not mistaken he's tuned the instrument down a tone as well.