It doesn't play on anything. It plays at the start of battle. Alas, Poor Queen
doesn't play on a Borg Queen ('cause she dead by that point), All Threes
doesn't play on your draw deck, Anti-Matter Spread
doesn't play on any specific opponent's ship. Attack Pattern Delta
doesn't play on a Tac Console or a BBD. I Do Not Take Orders From You
doesn't play on all your Treachery x2 personnel, Inside Operation
doesn't play on your infiltrator. Some of these play in the liminal space where interrupts materialize ("the table"? sounds odd but seems right). Some of them play "at
" a battle, which one might argue means the specific location, not "the table".
Either way, it's not playing on any specific ship, facility, personnel, crew, away team, or equipment involved in the battle.
Its effect is to prevent battle at the entire location for the reason Paddy stated. It's neither a facility, nor a site, nor a card that plays on a facility or site (see above), so when it says "there," it means "at the location of the battle."
Y'all looking for a loophole, and I admire that, but I don't believe there's any loopholes here. And I am pleased to hear that you all at least understood the intent out of the gate.
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