If you eat nothing but bok choy you'll be in exactly the position Andrew is warning about, ie., half-starved and miserable.
Your body needs energy from either carbohydrates or fat. Or both. If it has carbohydrates it will "refuse" to use fat for energy. If it has fat and no carbohydrates it will burn fat quite happily, converting the glycerol backbone to glucose if necessary (mostly, it isn't).
If you load up on protein while restricting carbs and fats, you will (a) feel like shit and (b) convert a lot of protein (very inefficiently) to glucose, which is a really, really expensive way of giving your body carbs.
Having said that, if you're eating plenty of fat (which is very energy-dense - you don't need much) then eating veg is an excellent way of filling your stomach with bulk, which will make you feel comfortably full. And of course you'll get your vitamins etc.
If you're working out hard, you can probably choose freely between any mix of carbs and fat and get broadly similar results. If you're not, and you're trying to lose bodyfat, you'd be better off relying on dietary fat for energy and eliminating carbs as much as possible.