You're correct. It's all about the relative motion between the strings and the pickup. If the strings held perfectly still and the body vibrated, you'd get sound because frame of reference A is still moving relative to frame of reference B, therefore from a physical standpoint, it's impossible for there not to be a difference if you make a change that effects the relative movement of the pickup. The real question is whether the difference can be heard. There's a couple reasons to believe the difference isn't audible. First, even the mounting ring or pick guard mounted pickups are moving along with the body of the guitar, they don't isolate the pickup from the body's movement. Second, the amount of movement in the strings is much, much greater than any movement of the pickup.
Yet another question is what would the difference sound like if it were loud enough to be heard? Maybe one way to find out wound be to take a guitar with two necks, mute the strings of the active pickup with your hand so that they're unable to vibrate freely, then strum the strings on the inactive side of the guitar. That should cause the active pickup to vibrate while it's strings remain fairly still, and you should hear the sound produced by the movement of the pickup alone.