There is much truth to this and it makes an important point. The crimes of the Nazis were many, varied, and hard to distill into a simple, concise, statement. In trying to do so, we may misunderstand the nature of the regime.
I think what happened for me, and I assume for millions of others, is that we started learning about the Holocaust during childhood, when simple explanations were all we could understand. As ten year olds we can understand, "Hitler was an evil man who hated the Jews and killed millions of them in his concentration camps. We call it 'The Holocaust'." (And, as an aside, we didn't use that word when I was growing up.)
Most people never learn much about history, and so never go beyond the ten year old version of the story. The reality is far more complicated than that. Hitler hated lots of people, and he used brutality against all of his opponents, and he, or at least his lieutenants that carried out the exterminations, had all sorts of justifications for why exterminations and mass starvation were justified under the circumstances. Reading about the Nazi era later in life was somewhat disturbing for me, because I realized that it wasn't as bizarre as it seemed, and bad stuff like it could happen again.
Meanwhile, though, the deniers pick some apparent inconsistency between the grossly simplified version of events and reality, and reach the idiotic conclusion that none of it happened.