Ahhh, I got it now.
Guitar Amp Basics has a little note at the bottom of the "Tone Controls" section explaining that the presence knob actually reduces negative feedback on the tubes for the frequencies above the treble-knob's range. Then I found The 'Presence' control? on "The Gear Page" in which John Phillips says:
The negative feedback loop in an amp is a sort of 'damping' (that isn't quite the right electronics term, but it will do) and makes the power section run more linearly, or 'smoothly' - by taking some of the output signal, running it 'backwards' (that's the negative bit) and re-applying it to the input, as a sort of self-regulation.
If you put what are essentially tone controls into the negative feedback loop, you can affect the degree of smoothing at those frequencies. Presence affects the top end, resonance the bottom end. Basically turning either of these 'up' actually turns those frequencies down in the loop, and allows those ranges to be less restricted. They don't sound the same as simple bass and treble controls because they affect the dynamics of those frequencies more than the 'amount' of them - which is why you tend not to hear them doing very much at low volume, but once the power section is really cranked they can become more effective than the normal tone controls.
Wikipedia has an article mentioning it too that says Fender came up with it first and, again, it's negative feedback for the very-high frequencies:
The original Fender presence control acted upon the amplifier's negative-feedback loop. As the level of "presence" was increased, so more and more of the higher frequencies in the negative-feedback loop were dumped to ground, leaving the low and mid-range frequencies. Increasing the presence resulted in there being less and less negative feedback on high frequencies. The effect varied according to amplitude.
That makes sense; By reducing the feedback, the sound in that range will not be clamped as much as the circuit tries to avoid run-away amplification. The result is a minor boost in that frequency range.