Does milk tenderize meat?
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.