All gear, in this case let's consider just the preamp for sake of discussion, has an inherent noise floor (I believe Yamaha, for example, refers to this as "residual noise").
An amplifier amplifies everything that comes in; the preamp's residual noise and the signal. Residual noise is essentially a fixed value, the signal level can be varied using the volume control. Both get amplified equally when they hit the power amp.
So, by running the amp lower and the preamp higher, what goes into the amp is a higher percentage of signal to residual noise. Thus, what come out of the amp follows the same with a higher percentage of signal to noise.
I will grant you that on very quiet gear, which Yamaha tends to be, you'd be hard press to tell much difference in most situations. However, all gear and all situations are not the same in this regard. And, even though you may not hear the difference in your system the effect is still the same. Amp lower, preamp higher = better S/N ratio.