They could have known they wouldn't succeed but they could have decided their fiduciary duty requires them to either try or resign.
Yeah the minority share holders can’t sue them for not trying to do their job even if it lead to them getting fired. (They could have quit too)
If they truly believe the CEO was destroying the company/its value.
Didn't they craft themselves a nice golden parachute if fired? Then proceeded to kick off events that would guarantee their dismissal?
That's less fiduciary duty and more hacking a payday.