... That is an excellent commentary, Mike, by one of the industry leaders. If Dave Johnson says it, it is gold.
Let me just say that for the layman, or non-techie detectorist, sensitivity is a function of gain, otherwise known as amplification. Without the latter, you don't have the former.
For all practical purposes, detectors made today have a fixed power output, ie, they don't modulate the emitted signal strength. So the amount of electrical energy being induced into the ground is constant.
What they do is increase the gain, or amplification, of the receive circuits. This in turn increases the strength of the signal coupled back from the receive antenna portion of the coil. The higher you turn the sensitivity control, the greater the amplification of the receiver. This means you can (in theory), increase the detectors response to deeper targets, all things being equal.
It also means you subject the circuits (and the user) to ever increasing feedback from clutter (closely spaced targets - both good and bad ones), high concentrations of soil minerals and random circuit noise. At some point, you overload the receiver with too much amplification and these things cause falsing and chatter as a result. This can occur with all detectors and each model reacts differently to this effect.
It is often equated with driving in a thick fog with your headlights on high beam. You are blinded by the increased light reflected off the fog, and so your vision is actually worsened.
There is a fine balance one must strike between running the gain high to get good depth, while still reducing the detrimental effects of these negative influences. For most people, it means cranking the sensitivity until the falsing and chatter begins, then backing off a notch or two until the detector quiets down to tolerable levels.