simple one-liner question, but the answer will take a few more

To me (this is something I strictly theoretically deduced) the keyword is "apparently"...

Way I see it, and knowing what I know about combustion processes under various conditions, the following is most likely to be what is actually to happening:
In a gasser, the apparent edge of "optimal", smack in the middle of "too fat to run properly" and "too lean to ignite" (which is where we all want to run our engines, because that is where they make the most power), is in the ratio of air/fuelVAPOUR. The liquid fuel does not take part in the ignitability of the mixture. Liquids do not burn, only their vapours. So the better the evaporation, the leaner the absolute ratio can be while maintaining optimal ignitability. The poorer evaporation, the richer the absolute ratio has to be in order to maintain that ignitability.
If you ever wondered why old cars had a choke (whether auto or manual) and apparently needed a richer mixture for a cold start, now you know...

The spraybar itself, without the solenoid, does a poor job in atomizing the fuel, so not all fuel evaporates. That means you need to increase the total amount of fuel in order to achieve the correct, ignitable air/vapour ratio.

But once that ignition is achieved, and the charge is burning, the heat will instantly evaporate the liquid fuel, which has the effect of adding fuel to the fire but not oxygen. And when that happens, the burn gets rich and sooty.
What is worse, is that this remaining liquid fuel is still mixed with oil, and logic says that those tiny droplets consist of a fairly "fat" mix, because the oil does not normally evaporate.
So let's assume, we have a 10:1 fuel oil mix, and 90% of the fuel evaporates on its way to the combustion chamber. That means that basically the remaining liquid fuel is a 1:1 fuel/oil mix.
That causes the droplets of this fat mix to "explode" and burn on the surface, causing that dispersed oil to overheat and decompose (and maybe a bit of it burns, who knows?)
Lots of soot is formed in this rich burn, and the soot is formed IN a cloud of dispersed, burning and decomposing oil, so that oil residue will be black and tar-like, because its detergent properties will cause it to absorb the soot. The burn having excess fuel means there are combustibles in the exhaust gas, so there is some afterburning going on in the muffler as well (I have noticed that the solenoid also lowers the muffler temperature. Indicators are significantly reduced deterioration of the sacrificial pieces of silicone tubing for muffler pressure, and for example fingerprints do not burn into the surface anymore. Heck, I have even seen the presence of liquid water IN the muffler of a running engine, witnessed by a drop of grey emulsion coming out of the tailpipe )

Now we introduce the solenoid, and what that solenoid does, is it interrupts the fuel flow 25~30 times per second. The engine by and large requires the same amount of fuel, because the difference in consumption between pre and post solenoid really is not that large, from what I have seen about 10% or less (the only plane I actually did "test" this with, was the 5 cc fourstroke: it managed 65 minutes on 6 oz pre-solenoid, and a touch over 70 post).
But this means, that this "roughly the same fuel flow" has to not only happen in less time (meaning a greater velocity at the spraybar exit) it also is "chopped" which also promotes evaporation.

I have actually visually seen this effect when I did the first tests (a veco 19 running glow fuel and the solenoid) about 8 or 9 years ago.
Back then my at the time availlable camera did not allow me to record it on video, but what I saw:
The perry carb, as most of us know, does not really have a spraybar across the venturi, but rather a tiny nozzle that only protrudes something like 0,02~0,03" into the intake.
Looking straight into the intake of the Perry carb, running on the needle there was a jet of fuel visible that frayed a bit at the edges, but reached all the way to the other side of the intake bore where liquid fuel would splash against the wall.
When running on the solenoid, there was no jet of fuel visible, but a "misty area" in the vincinity of the fuel nozzle, and reached only roughly about halfway of the intake. In other words, a finer mist and a better mixing with the air inflow.

Back then, I did not bother myself with fuel consumption and such, as gasoline and spark were not yet even on the horizon for planes, heck, I was not yet even occupying myself with fixed wing period! So those observations are just what they are and back then I noticed the difference but never tied a conclusion to it, as the entire reason for testing this device was to get a glow carb for planes, to behave properly in a helicopter, running methanol and spark. I never actually finished that project by the way, marriage and life got in the way, but that is another story.

Getting back to the issue at hand: this greatly enhanced atomisation and thus evaporation of fuel, leads to a "fresh charge" that has the correct air/vapour ratio to ignite, and contains basically only an oil mist, without (or barely any) liquid fuel present before ignition. This means that when the charge ignites, basically not much happens to the dispersed oil, because there is no burning going on at the surface of the droplets. Thus the burn does not "richen up" after ignition (no soot) and the oil does not or barely deteriorate from the burn, and precipitates on the relatively "stonecold" (relative to the burn temperature) cylinder wall in basically the same conition it was when it was still in the bottle it was bought in. Oil does that, same like moisture from air condenses on cold beerbottles.

I have seen it in all engines where the solenoid was introduced, that the exhaust residue cleared up considerably. Not all the same, not every engine became "spotless" and I also cannot really put a finger on WHY some engines ran cleaner than others (I have for example three identical ASP FS52, they even run the same or equivalent props, 2 ran near spotless, one still produces a bit of dark exhaust residue, but even the two that run clean, do not run identically clean).

Whether the above is true, heck, I do not have X-ray vision, no engine with an observation port, or the possiblility to shoot a combustion process at a gazillion frames per second and stretch the event to a 5 minute affair to closely study, but the explanation is at least consistent with what is I know about combustion processes and combustion technology in general.