Lustig's premise (from this and other sources) is essentially: (translated for a techie audience)
1. There is a clean pathway and dirty pathway for converting fructose to glycogen in the liver. The clean pathway is easily overloaded by consuming a lot of fructose at once. ("A lot" being more than 12 oz of soda, roughly.) The key bit is that the bad effects are non-linear.
2. The dirty pathway produces metabolites that cause the body's metabolism to switch to an imbalanced state, which if not corrected, leads to metabolic syndrome and type-II diabetes.
3. The dirty pathway is similar to alcohol consumption, with similar long-term effects. This is why he calls fructose a poison.
4. Dietary fiber slows down absorbtion of fructose, thus giving the liver more time to process fructose using the clean pathway. So an apple (fiber!) causes less of a fructose overload problem than a similar quantity of apple juice.
From this, Lustig hypothesises that metabolic syndrome is primarily caused by overconsumption of fructose, and that a diet that has low or zero fructose and high in fiber will correct metabolic syndrome. This is a testable hypothesis, and should be relatively easy to test, even by individuals.
My added notes:
1. There's lots of talk about "sugar", which is dumb, because "sugar" means different things to different people. Lustig means "fructose", which is present in sugar, HFCS, agave nectar, honey, all sweet fruits, fruit juices, etc.
2. Everyone's body, lifestyle, eating habits, exercise habits, and metabolic syndrome level is different, thus everyone will respond to fructose (and indeed any food) differently. If you care, learn how food works in your body and create a diet that fits your needs. And especially, don't extrapolate from your own experience to all people.
3. Several fad diets of recent years fit rather neatly into Lustig's recommendation, including Atkins, South Beach, mediterranean, raw vegan. If you care, find one that works for you.