The sensitivity control only changes the amount of gain (or amplification) on the received signal from the coil. The higher you amplify a signal the more noise and distortions found in it are amplified, so there comes a point (due to EMI or ground minerals) where the detector can no longer process the actual target signal due to the other white noise in the signal being amplified too big and thus as strong as a normal target signal would be. Sensitivity control is used to increase this amplification, and it's best point is where the target signal is indeed stronger but the white noise due to EMI or ground glare isn't also increased so high that it is strong enough to be noticed and caught up in the attempt to process the target signal. The white noise is always there. It's just a question of if you are increasing it's strength with the sensitivity control high enough to a point where it's too strong for the machine to still ignore and not react to.
Think of it as trying to zone in on one conversation in a room using a hearing aid. If you increase the sensitivity too high instead of just hearing the one person you are talking to you are now also hearing the conversations of everybody else in the room. Turning it down to the right point makes you better able to hear that person and, while the others are still talking around you, the volume from their conversations hasn't been increased enough for it to become a distraction to you.
I highly doubt the volume control does any kind of signal boost. However, I can see where it may in fact boost the weakest of audio signals for you to hear. With it turned down too low perhaps there is a cut off point where a weak audio signal won't be amplified and sent to the speakers. By keeping it full blast you insure even the lowest of audio signals are let by and amplified in volume.