Papillon
I agree with your line of thinking,but the use of you in the letter is ambiguous and needs clarification.
I agree that BA are not stupid and would not penalise working crew but it does need an explanation.
Either meaning is a winner for BA
If you(singular) strike you lose benefits.BA Don't careYou are a striker.WIN
If you(majority)strike then every one loses.Onus on the crew to return a no vote.Battle fought amongst crew.WIN
It is a very well thought out plan.