He may not, but I have seen a board threaten a CEO in a situation like that. It never came to a lawsuit, the CEO stepped down but this sort of thing definitely can happen depending on how bad the situation is.
Investors sue all the officers all the time. United Airlines, Ebay/Craigslist, Skype, non-profits, etc.
Suppressing systemic sexual harassment violates his duty to report management problems to the board. Same with any meetings with Otto's founder a week prior to them leaving Google and founding Otto.
