Sorry for not responding until now, Dirk and Paul, but I - personally - do think it credible that Dr Best did this.
Not because I know any more or have access to any sources that others do not.
But because of what - little - is known of his nature, as shown in the above references.
He made an appearance in a biography of Erik Scavenius, Danish former Foreign - during the First WW and early part of the Second WW - and later Prime Minister, before the Danish Government were replaced by direct German military rule -
https://en.wikipedia.org/wiki/Erik_Scavenius - there appeared to have been an affinity, almost friendship between these two - otherwise very cold blooded - men.
Whether he personally told anybody or authorized of what was to be, is hard to tell more than 70 years later, with little if any written evidence in appearance, and very few surviving evidence.
He could have done or authorized it, as at that time - August-September 1943 - it might have been clear to him that the end of Nazi Germany was near, and this might look good on a future CV - but at the same time not to be too near - just in case ...