What he calls "the origin of this lie" was the book written by Erich Kern in 1948,Der Grosse Rausch.The Viennese journalist Kern had served with the 4th Battalion of the Leibstandarte and for whatever reason sensationalised things.
This supposed slur on the name of the Leibstandarte was taken up by Rudolf Lehmann when writing its definitive history.Having scoured the records held in the Bundesarvhiv-Militararchiv at Freiburg im Breisgau and found no evidence of any such order having been given,he then went to the length of placing the matter before the State Justice Adminstrative Department(Landesjustizverwaltungen) in Ludwigsburg and obtained the reply from them that no such execution had taken place between 16-18 August 1941,the dates which relate to Kern's description.He describes Der Grosse Rausch as a "commentary",a free representation by the author(and with no documentation).