His audience certainly isn't a gear forum with people's who's hobby it is to chase 1 db in tone difference.
Forget about comparing single coils vs humbucker, passive vs actives. If you compare humbuckers for a moment you can see a few dB in broad difference in BMT. Pickups also act like 2nd order LPFs, so you can change the resonant peak freq. however, relative to the effect of the BMT knobs on your amp, a boost pedal, or an EQ pedal the differences bw pickups are much more subtle.
The question of the video, isn't really what the hyperbolic video title suggests. It's not that pickups don't change the sound it's whether it really matters relative to all the other stuff that make much more drastic changes. The answer to that question is, to a guitar hobby basement dweller, yes, because what else would they spend their time and money on.
So if they matter to you, then they do.