I've always envisioned it this way... the wood removes from the strings (or enforces in them) certain harmonics for every note on the fingerboard. The wood thus tells the strings how they can and can't vibrate, and the pickups reproduce this through the lens of their particular impedance, magnetic strength, position along the vibrating string, etc.
BTW, anyone ever notice how playing the highest notes on the guitar through the neck pickup sounds almost as bright as the bridge pickup? In a sense, your fingers are fretting and creating another "bridge" very near the neck pickup, thus making the harmonic balance more like it is when using the bridge pickup.
And I think the "bridgey-nes" and "necky-ness" of any pickup changes slightly for each position on the fingerboard. Say you play through the bridge pickup and fret at the octave: if the bridge pickup is positioned at 1/8 the full scale length, it's suddenly "hearing" the strings at 1/4 of the scale length (because of where you're fretting), thus picking up a different harmonic balance relative to when you play open.