Ironically you're making an assumption, speculating, and maybe they do know that for a fact - but we just don't simply know why they'd know, or if it's true. The best you can say is we don't know for sure.
But considering the board initially fired him for being dishonest/lying in an ongoing fashion, and the board wouldn't do the firing without evidence they could back it up with, it's not so hard to extrapolate that a return would be conditional on a deeper investigation and "full" cooperation.