Two areas of interest regarding BASSA/Unite's statements:
The first of amusement:
British Airways rejected our formal offer. It therefore need no longer concern you or require your consideration any further. They simply will not accept it. End of discussion. (emphasis added)
I truly chuckled when I read the above quotation. Of course they don't wish for their membership to consider their final offer. It was a cornucopia of self-serving rhetoric meant to strengthen the Union at the cost of their memberships well-being.
The second is one of logic. If BASSA is so concerned regarding their members getting a chance to have a voice regarding BA's final offer there is nothing restraining them from prepareing a survey of their membership. There are numerous ways this could be accomplished in a cost-effective and very swift manner.
If BASSA doesn't know how its membership would vote its because they are deliberately keeping their membership from having a voice.