If you knew anything about the media, which you clearly don’t, you would know Murdoch hates the BBC and wants to destroy it so his newspapers - i.e. The Times and Sunday Times - would absolutely and categorically never work with the BBC to time the release of two stories so one would cancel out the other. He just wouldn’t let that happen.
Plus, if you knew anything about politics, which you clearly don’t, you’d know Murdoch stopped backing Johnson months ago. He wouldn’t care about a story knocking him now because he has no interest in him as a political figure, much less want him reinstated as PM.
I worked in the media for 25+ years. This conspiracy theory shit is frightening.