The paragraph you quoted is utter nonsense.
Milk contains absolutely no factors which will tenderize anything. Tenderization is a process whereby protein strands are broken down, resulting in shorter strands, resulting in a more tender product. A lot of substances and physical processes will tenderize, to a greater or lesser extent, sometimes subject to other factors: acids, bromelain, a similar compound found in mango, physically pounding the meat, etc. Milk is none of those things.
Further, simply limiting the cooking temperature to under 212F/100C will not, in fact, guarantee a tender and moist result. To see this for yourself, boil a chicken breast in water or milk for a while. It will never go over the boiling point of water, but if you leave it too long? Dry, nasty chicken.
As Mike said in his answer, braising will result in a more tender end product; the length of cooking time plus the liquid medium helps to moderate the temperature and cook the protein very, very slowly. This retains more moisture within the product, and prevents protein strands from bunching up very tightly (which, really, is the same thing: protein strands force water out of meat as they constrict; prevent or ameliorate the constriction and you will have much moister and more tender meat). It is also worth noting that braising is always done at significantly below boiling temperatures; one braises at a simmer at most, more in the 60-80C range.
Milk is often used with certain proteins due to its facility in absorbing unpleasant odours or flavours. Liver is the classic example, but milk is also often used with sweetbreads and fish (amongst other things) to help draw off the funkier aromas before cooking. I do not know the specific scientific mechanism behind why this works; I suspect it is something to do with the fat molecules in the milk itself, which suggests that any fatty liquid would have the same effect.
So, for the short answer, see my first sentence.
Best Answer
I think what's really happening here is mostly physics, rather than any magical reaction between the meat and the "velvet" (i.e. egg and cornstarch; I'm going to use this term for brevity).
The largest effect is that the velvet adds a thin, clingy coating to the outside of the meat. When introduced to heat, that's providing a barrier to the movement of thermal energy into the meat proteins. The proteins in the egg are denaturing, the starches are gelatinizing, and that absorbs some of the energy that would otherwise have gone into your meat. The presence of sheer additional mass from the velvet also means that it simply takes more energy to raise the overall temperature. This means that the temperature increases more slowly, and can be better controlled (sort of like sous vide cooking).
As the starch gelatinizes, it's also forming a moisture-resistant barrier around the outside of the meat. That could very possibly prevent moisture from leaking out of the meat as it's squeezed out of cells with denaturing proteins. Ordinarily it would leak out into your poaching liquid (or wok if you're stir-frying, where it would rapidly boil off) but now it's trapped in the pieces of meat. This is also somewhat analogous to sous vide cooking, or maybe to poaching in oil - the food being cooked stays moist, because the water is trapped inside (by a bag in sous vide, by hydrophobic oil in oil-poaching) and has nowhere to go.
Another factor is the very gentle cooking being done, in a barely-simmering water bath for a short period of time. This is cooking the meat just up to the point of doneness, by doing so at a rather low temperature (say 210 F or so, compared to 500 F or higher for a properly hot wok) and only very briefly, with the velvet coating for additional thermal protection. After that, the meat doesn't really need to be cooked much at all - it can be tossed into a nearly finished stir-fry just to the point of being re-heated. That seems to be why this article tosses out this interesting comment:
I hadn't given it much thought before now, but that seems to match my experience in good Chinese restaurants, at least with certain dishes. Contrasting this with stir-frying sans-velvet, think about a browned piece of meat: the surface is covered with a delicious Maillard-browned crust, but those proteins have also been cooked to the point of losing their moisture. Even if the interior of the meat is moist, the outside's been dried, literally to a crisp. With velveted meat, that's not the case - each entire piece remains moist, and there's no browned, crunchy layer.
I'll be the first to admit that much of this is conjecture, but I think it provides a reasonable explanation for some of the processes that keep velveted meat moist. Might be interesting to dig up some scientific references on the thermal gradients of proteins vs. starches - I'll see what I can find.