I don’t think it’s downplaying or “sweeping under the rug of history” to state facts about the Nazi regime. They did not do things according to the letter of the law. They did a judiciary takeover, allowing illegal acts to happen, and they did seize absolute power, murdering political opponents.

None of these things were possible without a good amount of popular support. And a lot of the population stood by and watched it happen, or even endorsed it.

I do worry you’re falling into the ‘trap’ that neonazis set. Neonazis like to state these things (eg “there’s no written order from Hitler to start the Holocaust”) to deny other historical facts. It’s important you engage these arguments correctly. By arguing against these things being true, you’re falling into the trap, because by and large these arguments aren’t wrong. There is indeed no written order for example.

It’s really important that you deny that the argument even holds any relevance in the first place. It didn’t matter that there’s no written order, the Nazis did it regardless. The Holocaust being illegal does not matter. You can argue the complications of a dual-state legal theory that’s not explicitly codified, and you’ll get lost in the weeds because there’s enough arguments to be brought up there. Instead, you must argue the Nazis didn’t need it to be legal in the first place. Doing so renders the legality argument useless in the context of Holocaust-denial.

The legality aspect is an interesting debate. But be careful that you don’t accidentally legitimize its use in Holocaust denial.