The board cannot unilaterally decide the share price. The deal will only be finalized once, among other things, it's approved by shareholder vote. But that is largely a formality. The largest shareholders are going to be institutional and not ideological, and $54 is way higher than most (all?) estimations for Twitter's value. Incidentally the same reason that refusing this deal would have exposed the board to personal legal risk.

As for why it's fair - a share doesn't represent ownership of a company, it represents a voting share in an abstract entity. Normally these are pretty close to the same thing, but there are important distinctions - such as here. When Twitter goes private the abstract entity it used to be will cease to exist, along with all voting rights in such.