....and then realize only the "stopping" part is true (and not even that exactly in the case of a vehicle with regen braking, depending on the situation and how fancy your T/C S/C is). Anyone that claims that AWD doesn't aid with turning and maneuvering isn't giving you the straight story.
Now whether or not the extra benefit of the AWD is enough for a given situation when you have sub-standard tires, that is certainly in question. But that statement you quoted is misleading in that AWD in fact does increase your working traction, increases the friction you can utilize for directing the vehicle where you want it to go.
Given a road surface (pick compact snow, for example), and a specific tire, there is a number for static
friction. You can count this as a fixed number for the surface to tire interaction, as this number only depends on how the materials interact. The only way to increase this number is changing the road surface, or changing the tire.
Regen braking at all four wheels is potentially nice, but dangerous (Tesla rightly recommends switching to low regen in snowy conditions) and cannot increase friction. Your braking system utilizes all four wheels for stopping as well, and is suitable for the task. In both of these cases, it is indeed "braking" which if there is too much of will overcome the static friction, meaning sliding on the surface instead of gripping it.
At low speeds, I did mention AWD helps even for turning, of course.
As for turning benefits
above low speeds, AWD only helps if you are accelerating AND if your vehicle employs active torque vectoring (Model 3 cannot do this as it can't control the right vs. left power without using brakes). Many AWD vehicles disable either the front or rear drives at highway speeds anyways, and some suspect the Model 3 disables the front as well (I haven't seen anything conclusive on this). Turning while coasting or maintaining steady speeds simply has no benefit because the AWD is not sufficiently driving any wheels.
In fact, acceleration while turning increases the risk of breaking the static friction (starting to slide) because you're applying more force (the other forces are those bringing the car through the turn, which increase with speed through the turn). With FWD this means you lose steering. With RWD, you fishtail. With AWD, you flip a coin to see which end broke loose if not both!
Rally drivers indeed benefit from full time AWD with more complicated differentials, much of the benefit coming from acceleration. Cornering is helped too, but cornering rally-style on public roads might get some sirens coming your way (terribly fun though, isn't it?).
