Well no one cited the basic physics I was hoping for, or threw out a relevant equation or two but the general idea that the pins effect the mass of the bridge makes sense to me. The traditional analysis of a vibrating string assumes the end points are anchored and the only vibration occurs between the anchor points. Thus, the model does not allow for any effect from, for example, the bridge pins. I'd say in this case the model does not completely match reality.
That's correct that model is incomplete.
The erroneous assumption in that model is that vibration
only occurs between the anchored end points.
Actually, the issue is that
only the vibration created between the anchored endpoints is responsible for pitch of the string at a given tension.
BUT:
Strings also vibrate in the area between the saddle and the bridgepins as well as the nut and the tuning posts.
The density of the pin material will affect how much of that vibration is damped (Absorbed by the pin) or reflected into the bridge and bridgeplate (and thus the top).
Similar to the principle of a glued neck allowing better transmission of vibration between neck and body than a bolt-on neck which is usually assumed to have less efficient transmission of energy between mating surfaces.