re: I'm listening to the Rise and Fall of the Third Reich

First of all, the blame for who set the Reichstag fire is not settled history, regardless of what Shirer wrote.

The lessons to be learned irrespective of who set it is that the Nazis used it as the catalyst to massively expand their centralized state powers under the auspice of countering an imminent insurrection/revolution. A foreign Marxist was arrested, tried, and convicted of the crime. The Nazis attempted to convict a wider Communist plot in the fire but the legal proceeding only succeeded in convicting a single revolutionary Dutchman with a record of arson and who confessed to the crime. As I recall he was not entirely mentally fit.

It's more likely, and fittingly for comparison's sake, a tale of exaggerating a one off incident into a coordinated and widespread conspiracy blaming political opposition and using this narrative to destroy said opposition's legal and practical means of exercising their political dissent.