The boards mandate is one of fiduciary duty. Bluntly, that is not a mandate to maximize shareholder value, especially in the short term.

They do not have an offer that will maximize shareholder value - they have an offer that will increase it.

Words have meaning and concepts have definitions. They are not arbitrary of flexible for the sake of making the argument you want.

The BOD's responsibility is to the company, a public company's responsibility is to the shareholders - this difference matters.

Cornell's legal information institute provides a nice and cited set of definitions (albeit in legalese) - https://www.law.cornell.edu/wex/fiduciary_duty