There is, of course, the suggestion that the body that was used was that of a drowned sailor from HMS Dasher that sank off the Scottish coast at just the right time. That body would have been in much better physical shape than Michael's and much more convincing because death had genuinely been from drowning.
Conspiracy theorists have it that the true identity of the corpse was not disclosed because it was"simply not British", even in wartime, to go round pinching bodies that didn't belong to you albeit for such an altruistic reason. Allowing it to be assumed that the body was that of someone from the lower social orders and, whether we care to admit or not, less valued may have simply been a device, a double bluff to fool the Germans and the British public, in order to avoid controversy.
Short of acquiring some DNA from the remains of the man who never was and comparing it with samples from relatives of some of the Dasher candidates( there was more than one) I can't see how we can resolve the problem.