Salt in the water lowers the boiling point of water. the more salt added,the lower the boiling temp,but this only works up to a certain concentration of salt to water. 1 teaspoon salt to one quart water will lower boiling point 22 degrees to 190. The reason you want to lower the boiling point is to lessen the chance of the sulphates of iron and copper from precipitating out of the egg yolk. Since copper sulphate is bluish tint+yellow yolk=green ring between yolk and albumin(white). Iron sulphate is greyish-brown tint+yellow yolk=black ring.
Distilled white vinegar is used because,the acetic acid present in the vinegar,breaks down the carbonate molecule,thus releasing the calcium and making the shell easier to peel since it is now thinner than when you started.
The advice to plunge the cooked,not boiled,eggs into iced water is valid since this causes hot/cold surface tension that cracks the shell;thereby assisting in easier peeling of the fresh egg.
All y'all take care.