As for Rabbi Sacks statement. I heard him say that exact quote on Zev Brenner is the Rebbe studied Hitler. It’s possible that in writing he said it differently.
If indeed Rabbi Sacks said that, I apologize for accusing you of making it up.
The point remains that Rabbi Sacks never intended that the Rebbe did some “Hitler study,” rather he was saying a cute vertel about how after the Holocaust, the Rebbe showed love for every Jew like Hitler (l’havdil) showed hate.