Fun thread!
Experience and personal opinion aside, this argument, like most, can be settled with a basic understanding of PHYSICS.
1. A pickup transduces the sound of the vibrating string into electrical potential.
2. The string, being physically connected to the body and neck, transfers some of that kinetic energy back to the guitar itself (and to the player's hand, and the air surrounding the string, of course).
3.
Newton's third law of motion tells us that the guitar is sending a corresponding force back into the string, which we can infer would affect the string itself and how it vibrates.
4. Therefore, the guitar itself, and not just the string, affects the output of the pickup.
I figured this was pretty much common knowledge amongst all but the most inexperienced guitarists. It's pretty much self-evident that acoustic tone affects electric tone, but I guess some people just don't get it.
Put it this way: if the guitar itself made no difference, we'd probably all be playing plastic guitars, or whatever the cheapest material that meets the structural requirements of a guitar is.