My guess is that it works a bit like the input trim you described, but it’s not continuous.
If you just put some high gain amp and a cab on row 1, you can hear the noise floor even without a guitar.
From 0 to 9.3dB you turn up the gain and you can hear the noise floor get louder. At 9.3dB, like DavidRSTV described, you can suddenly hear the noise drop. There are more breakpoints like this somewhere around 12+dB and after that.
So I think the QC does only increase the gain on the digital side up to a certain limit and then increase the analog side gain step-wise to maximize the dynamic range and compensate on the digital side.
In other words, the input gain grows as you turn up the knob, but the analog input signal is “rescaled” every few dB.