While it's a fireable offense, my experience with senior management has been that the company is more than happy to help cover it up for them... until they do a bad, and then it becomes a quick ticket to can them without having to admit the real reason for canning them.
Seems like that could actually map pretty well to this case.
That's what everyone keeps saying. INAL but that would give any fired executive hella leverage when the board finally decide to unveil what they've been hiding. I mean, they'll go to discovery and ... perjure themselves? Really?
What claim would the executive have? They can be fired by the board for any reason (except for a few explicitly prohibited reasons), so "they lied about why they fired me" doesn't work as a claim unless you're alleging the real reason is because they're racist or something similar.