Sam2: I am moche on your suggestion that any Rishon or Achron would stoop to using lies to defend a position. Or for any reason at all.
I will just say that my position is that when it comes to someone acknowledged as a gadol, there are no boundaries to the emunah one should place in him. For me, these three gedolim have more than enough status to warrant emunas chachamim. I don’t need to understand the how or why in order for me to accept their words.