Not the way it works, Mr Ford.
A so-called "logical inference" only comes into play when there is not sufficient evidence to justify a conclusion. It's a poor substitute for actual evidence.
A logical inference comes into play when there is sufficient evidence to justify a logical inference. Such is the case here.
Rejecting this logical inference (in the absence of any counter-explanations of your own) is tantamount to saying 'I refuse to accept the claim of a cover-up because you cannot provide the kind of full documentary record that would have been available had there not been a cover-up'. It's a heads-I-win-tails-you-lose style of argument more usually associated with cornered LNers.