Water intoxication kills primarily by diluting the blood and causing hyponatraemia (low blood sodium). Water then moves by osmosis from its area of high concentration to its area of low concentration - from the blood to the intracellular space.
The swelling the water causes is called oedema (US - edema), pulmonary oedema in the lungs, cerebral oedema in the brain. Cerebral oedema results in confusion, convulsions, coma and ultimately death.
The figure of 8 gallons/hr is extremely high. The "lethal dose of water" could be very much lower, though I would hesitate to put a figure on it. Leaving wet, dry and secondary drowning aside and considering oral or intravenous fluid, the kidneys of a healthy adult can excrete a maximum of less than 1 litre/hr. This figure may be very much reduced in patients with renal or heart failure in whom fluid balance is notoriously difficult to maintain.
Of course, this does not mean that drinking more than 1 litre/hr will kill you, particularly if you are fluid-depleted. Dehydration is a much more common killer. Homeostasis is quietly effective even in the face of gross physiological insult. Nonetheless, there's a limit.
Drinking large volumes of pure water in a short period, particularly while electrolyte loss is occurring (heavy sweating, bleeding, vomiting, diarrhoea, burns etc.), is dangerous. It remains a major cause of death amongst children worldwide following diarrhoeal illness - though a massive campaign by the UN and WHO has helped. It's what kills people in those inexpressibly stupid water drinking contests. Famously, it's what killed Leah Betts, in whose case excess water consumption was compounded by drug-induced failure of normal homeostasis (see SIADH).
In everyday situations and in normal quantities, pure water is fine for hydration - healthy, readily available and cheap. Dietary sodium intake is almost always more than adequate. When large-volume fluid replacement is required acutely, particularly when electrolytes are being lost (see above), it's advisable to replace salt and sugar as you go, with isotonic rehydration solutions. You can buy these as sports drinks or sachets of oral rehydration salts. Alternatively you can make your own with 8 level teaspoons of sugar and 1 level teaspoon of salt per litre of water. Half a mashed banana adds flavour and potassium.*
Everything2 medical disclaimer
* - http://www.rehydrate.org/solutions/homemade.htm#recipes
Thanks to doyle for advice on a few changes.