Yes ...very amusing...and true. I would however argue that in the absence of any evidence HMRC can prove HMRC have to accept your response. innocent until PROVEN guilty BEYOND ( emphasis) reasonable doubt.
HMRC can make an assessment if they have reason to believe that income has been omitted or understated. All that is needed is a reasonable belief, and having assets beyond your means could support such a belief.
In a tax appeal, you are the appellant. It is your job to show the assessments are excessive, it is not for HMRC to show that they are not. Beyond reasonable doubt doesn't come into it, the standard of proof is the civil standard - the balance of probabilities.
In answer to the question "how do I prove a build-up of assets", it should not be too difficult to prove you received an inheritance.