The problem isn't so much that we drink an excessive amount of water as it is that we drink an excessive amount of water in a short period of time.
Every so often there are bets on who can drink 1 gallon/3.8 liters of milk within 20 minutes without vomiting. In nearly all cases, whoever drinks that amount of milk in 20 minutes vomits and loses the bet. It turns out to be true for something as simple as water.
Why would someone vomit after drinking that amount of water rather than milk in 20 minutes? You touched on it in your post: the body can't adjust its electrolyte balance in so short a time for so much fluid. It throws everything out of whack. 1 gallon/3.8 liters of water over 2 hours is doable; but in 20 minutes, that is asking for trouble.