Harris has identified a real problem, rooted in the idea that facts are objective and values are subjective.
Harris rejects this facile opposition in the only way it can be rejected—by pointing to evaluative truths so obvious that they need no defense. For example, a world in which everyone was maximally miserable would be worse than a world in which everyone was happy, and it would be wrong to try to move us toward the first world and away from the second. This is not true by definition, but it is obvious, just as it is obvious that elephants are larger than mice. If someone denied the truth of either of those propositions, we would have no reason to take him seriously.
These cases show that the idea of truth applies to values as much as it does to facts—but as with facts, the idea is not limited to obvious cases. There are many questions of value whose answer is not obvious, and about which people disagree, but that does not mean that they do not have a correct answer. As Harris points out, exactly the same can be said of historical and scientific questions: one should not confuse truth with what is known, or agreed on by everyone.