What does splashing in a shot of white vinegar to the simmering water do when poaching an egg?
Is it for taste or is it supposed to react in some way with the albumen?
Egg whites need to be heated up to a certain temperature in order to coagulate ("set").
Lowering the pH (increasing the acidity) of the cooking liquid is one way to lower the temperature required for coagulation of the egg whites. So, in a way, this does prevent "feathering" of the eggs, but not because of any direct reaction; rather, the reason the eggs feather less is because they have less time to feather, because they don't need to get as hot.
Any acidic liquid will have a similar effect. White vinegar is probably the most effective, but you could also add lemon juice or wine to the poaching liquid. In fact, eggs poached in red wine sauce ("Oeufs en Meurette") is quite a popular preparation method.
For reference, the coagulation temperature is also proportional to the salinity (add salt to lower the coagulation temperature, add sugar to raise it), and inversely proportional to the number of eggs used (more eggs = lower coagulation temperature).