I'm not sure what is needed from the board here, but I think there's a difference between a board recommending something, and having a fiduciary duty to present an offer to shareholders. Where are you reading that this needs the board's blessing?
If the board doesn't approve, he goes to the shareholders and asks them to replace the board (or becomes such a large shareholder he can do it himself).
Twitter's bylaws contain anti-takeover provisions which would make a hostile takeover difficult. In their latest 10K they list these provisions which includes "authorizing 'blank check' preferred stock, which could be issued by our board of directors without stockholder approval and may contain
voting, liquidation, dividend and other rights superior to our common stock". So if Musk attempted to get shareholders to vote out the board, the board could issue preferred stock with voting rights which could dilute Musk's votes.
People complain about fiduciary duty lawsuits but "authorizing 'blank check' preferred stock, which could be issued by our board of directors without stockholder approval and may contain voting, liquidation, dividend and other rights superior to our common stock" and then using it to go against a vast majority of shareholders could result in a huge court fight.
