From what Broughton has been saying, it's essentially pretty straight-forward:
A majority of the board can approve a sale, and they have.
Broughton is the only one who can change the board (this is apparently written in the terms, H & G can't change the board, despite their efforts to do just that).
And with the publicity the sale has had and with the two competing bids, H & G aren't going to be able to argue that the sale undervalues the club.
Basically, when Broughton was appointed it was ensured that he would be able to do his job and sell the club without H & G changing their mind and refusing to sell if they didn't like the eventual result.
So unless there's a loophole somewhere - which seems unlikely given that efforts were made to prevent exactly that - H & G have no chance.