The fundamental error he is talking about is the belief that the self exists intrinsically, an immutable object that depends on nothing outside of itself. This is a fundamental error because the first moment of self awareness gives rise to the false belief that the self actually exists in the way it conceives of itself. The Dalia Lama isn't trying to dumb down Buddhism or appeal to anyone. He is attempting to explain one of the Buddha's insights from 2,500 years ago, and insight he verified with his own meditations -- an insight anyone can verify if they meditate deeply enough with some focused understanding. It's an insight at the core of Tibetan Buddhism.

In Buddhist practice, the shortcut to Enlightenment is to fully realize the nature of emptiness. The emptiness of Self and the emptiness of all objects. All human constructs are products of the mind. The debates and distinctions between various philosophies within Buddhism are extremely narrow and focused on the relationship between objective reality of the outside world and the subjective reality of our inner world. One one extreme, they recognize that no information on the outer world comes to us unmediated by the mind and senses, something neuroscience has also demonstrated. On the other extreme, they recognize that there is an outside world that the mind mediates, and this outside world would exist whether or not a mind perceives it. The first is arguing there is no intrinsic existence (which is what the Buddha taught), and the second is arguing the outside world exists intrinsically but we have no direct perception of that due to our mind's mediation. There isn't any real difference between the two outside of semantics.