The propaganda machine relies on a never ending stream of groups to be labeled and attacked.
Without knowing who to even target with smear campaigns, their power is limited yet again.
Thus, my thought is that the obviously false VP speculation is meant to lure the reactive side of Trump, so he says something like "I would not pick Birdbrain, I would pick [insert name here]", thus giving them another name to attack and write articles about.
Without knowing a VP pick, assuming continuance of government, they can be blindsided. In a world of double/triple agents, smoke-and-mirrors and illusion, Trump's chosen successor could be anyone.
When you deprive the propaganda media of names and groups to attack, their postings get more and more ludicrous and incomprehensible and eventually due to their nature they end up eating themselves like starving hyenas who decide to turn on the other hyenas, an ouroborous of spite and decay.
It is sound strategy to play your real cards close to your chest in the fog of war, while letting your own enemy destroy themselves through their own panic.
Criminals are a cowardly and superstitious lot.
At first no but then eventually yes.