I can understand and appreciate what you say but, as it stands, yours is a hypothesis. With genuine respect, it doesn't provide any evidence to contradict von Rintelen's account - and he was, after all, a primary source, whose account was publicly endorsed by the head (or close to it) of the British secret service and one of his deputies.

Now, I can understand that Hall might have been wilfully deceiving von Rintelen; however, there is no evidence that this is the case nor does Hall seem to have immediately apparent motive of hostility towards his former adversary. In fact, strange to say, there is primary evidence that after the war, Admiral Hall and von Rintelen were the complete opposite of enemies but close and mutually trusting family friends. Have a look at this. http://www.time.com/time/magazine/article/0,9171,769867,00.html Interesting, no?