Absolutely right. I am an (wait for it...) Eggspert in this field as I have cooked myself an egg of some kind almost every day since about 1997. The difference between a freshly laid egg and a "fresh" supermarket egg can be several days. Fresh eggs hold together tightly and older eggs spread out all over the bottom of the pan. Vinegar reacts with the outside of the egg white to form a "skin" when you put it in the water so it holds together better. Having said that, I quite enjoy the subtle vinegar taste so I normally put it in anyway.

My method of poaching is to swirl the water and crack the egg very carefully into the centre of the whirlpool if there are any doubts about freshness. This also helps to hold the egg together. I then leave it simmering for a couple of minutes, and lift it very gently with a slotted spoon - you can tell how solid the egg is by the way it moves as you lift it out of the water. That way you can judge the consistency of the egg as some people like them firm (but with a soft yolk) and some prefer the white to be a bit runny.