That, frankly, is bollocks. For a start, "drinking water is good" is debatable because if you drink too much water it can kill you. Too much vitamin a can kill you as well (this, for the sake of trivia value, is the reason the indigenous peoples of the Arctic eschew the liver of the polar bear: it contains so much vitamin a that it is poisonous). Drinking water is good if you are thirsty.

You're not going to poison yourself with carrots, but if you already have a sufficient minimum of vitamin a in your diet then adding carrots to your diet won't help your eyesight one jot. There is a popular myth - and I'm not expressing an opinion as to whether or not you subscribe to it - that more vitamins = better, and it's not the case.