While the ignorance is remarkable, and the fact that it all made it to broadcast is similarly remarkable, I don't think Nakajima is completely responsible for all this commotion.
What most people seem to have a problem with is that the "great people of the world" theme of the segment was used in regards to Hitler. A better title, maybe "important" instead of "great" may have helped with that, as I don't think anyone can dispute that Hitler was an important figure. But with the light atmosphere of the show, bringing Hitler into it was ill-conceived.
But, as I mentioned, referring to him as "Hitler-ojisan", or "Uncle Hitler" was pretty dumb. In the context of calling all the historical figures in her segment by familiar names, like "Marie-neesan", it makes some sense, even if it's of questionable taste.
As for Nakajima not being entirely at fault here, I do think that a certain amount of blame should go to the adults who should have known better. Even if there were disclaimers from Nakky about Hitler, they could have been edited out for time. Even some articles about this episode seemed to acknowledge that certain things that seemed clear at the time are not always communicated easily through television. It seems to me that there is enough blame for a bunch of people and the show staff and the network people dropped the ball on this one.
In any case, the network issued an apology and I think H.P. did as well, so whatever. It's just another case of ignorance, inattentiveness, and bad judgment that allowed something to air that shouldn't have. Eh, that's television for you.