Your right MrD, they can’t.
By reducing that 2v source with the volume control of an active pre, just shunts part of the 2v to ground. The other part being used (just as "distorted") goes to the preamps volume control then the gain stage, "yes" to be boosted back up again along with it’s own distortion and noise also.
Some preamps are designed to have very large s/n ratios and very large voltage swing range capacity. And then the designer of the circuit puts sort of passive volume pot implementation -in front of the high gain preamp.
This results in a far higher level of signal quality on the output, with regard to preserving micro differentials in the signal, which is where the music works for the human ear.
Some tube preamps are more likely to be designed this way.
Or, some preamps are designed so the volume pot is part of the gain of the circuit itself. I believe that Charles Hansen made a version of such topology in one of his SS preamp designs with Ayre. A switched resistor circuit where each step was optimized to provide best low distortion and highest fidelity. Not just individually gain stepped but individually tweaked on each of those steps. (IIRC, that is, source: interview with Charles at Stereophile)
The one you take note of, which is the most common way to do it for reasons of a ’safe’ output section, is also the lowest fidelity way to set up a preamp circuit topology. The variable loading does indeed change the transient distortion of the circuit, and it also makes the output sensitive to the cables and input it is hooked up to, in a way that is non linear as one scales through the volume settings.
eg, the one with the hardset gain with the input being varied via a potentiometer at the start, that one... is more linear and constant in it’s coloring of the sound signature, as one scales through volume level changes.
Most (IIRC) of the Bruce Moore tube circuits were set up this way. There is a danger aspect as a potential problem, though, as the full gain is always applied to the amplifier inputs, via the preamp circuit.
So, one can accept the cheaper and easier to implement most common design method (volume pot just before preamp output) and have mediocre warmed over sound quality ...or.... play in the danger zone and have a notably greater fidelity in ways that matter to the human ear. (volume pot at front of full gain output)
I made that trade off over 30 years ago, and the cost of problems that have happened, over the years, was less than the cost of one single item upgrade. Less safeties on the system (DC or full scale output issues, etc) and more care needs to be taken, but....the pay off was over 30 years long, on a key point in fidelity. And that was priceless. Priceless.
Essentially, it’s too bad more people don’t understand how fidelity in audio works. It’s not all that simple...
After trying every active topology known to humanity, I gave up at the max grade preamp level of a customized three chassis MFA ’Venusian’ preamp (capable of over 165Vp-p into a standard load!), and went to passive circuits, but only when done via the liquid metal design we have on offer. IMO and IME, active is too complex and too colored. All of them. 100% of them. Even simple buffer circuits, even though they generally exhibit the least harm...
In my personal experience a liquid metal passive preamp defeats all passive contenders and all active contenders at any price. At the $10k level, at the $50k level, no matter. Additionally, the consensus on that, within the group of people who have actually heard such an arrangement of gear with the given specific passive preamp... is rather high. With zero caveats. How? the liquid metal does not behave like wire, on the fundamental scale of what impedance in dynamic living terms --actually is. high correlation on it being best? let me clarify: Hundreds of people, and maybe three or five disagree.
But this as a pronouncement, depends upon the rest of the system, all the individual components, of source, cables, speakers, etc.....and most importantly...the wiring of the mind and ears of the listener....all being up to snuff, in being at the center of the maelstrom of what each is required to do with regard to projecting and exhibiting (and hearing/realizing) the maximum fidelity of signal.