I hear this from time to time and wonder what makes people think the wood in their guitar has anything to do with how a pickup works. There is nothing about the wood that transfers into the pickup turning a string vibration into an electrical signal.
The wood a guitar is made of effects the resonance, sustain, and other subtle characteristics of the "quality" and/or "color" of the string's vibrations. Similarly, strings of different guages and/or materials that are tuned to the exact same pitch will also have subtle differences in "color". So your guitar combines many different materials that together generate the "tone".
Strictly speaking, the movement of the metal string within the magnetic field of the pickup is what gets converted into an electrical signal. However, passive pickups are much more sensitive to subtle variations in string vibration than active pickups. This is because a passive pickup utilizes a "natural" magnetic source whereas an active pickup utilizes an electromagnet. As a result, the active pickups are essentially amplifying the vibration of the string, adding their own color and distortion. This is why actives are ideal for high gain applications. Contrastingly, passive pickups translate the "tone" of the guitar and all of its components (i.e. tone woods) much better than active pickups. Furthermore, the signal generated by a passive pickup is directly effected by how it is mounted and its surrounding tone wood because those materials are also vibrating and resonating with the string. This causes very subtle changes in the magnetic field through the vibration of the magnet, which in turn effects the overlap of the waveforms, creating some constructive and some destructive interference. This directly effects the perceived "tone" of the guitar/string/pickup combination. An electromagnet, however, creating considerably stronger and more uniform magnetic field, negates most of this effect. It essentially normallizes the generated current, which is precisely why it makes a crappy guitar sound good and an extremely nice guitar sound the same as the active equipped crappy guitar.
The fact that different players and luthiers all over the world have preferences for and utilize different materials in electric guitars is not an accident. There are distinct, measurable differences between different combinations of woods AND pickups.
And for the record while I am not a luthier I am a grad student in physics, so as a 30+ year guitarist I've always been fascinated by the physics of the guitar and so I've studied it pretty extensively.