Airiam said (paraphrased, probably), "I will open this door and kill you. Then I will complete my mission, and destroy Discovery."
They believed her, and she was seconds away from either resuming or finishing the download.
She stated that Control was overwriting her motor functions so she couldn't control her actions. If they'd beamed her to the brig or sickbay or wherever, as soon as she was able she would resume the mission to download and transmit the sphere data. There was no way to win (and Jim Kirk was apparently unavailable

).
That's how I interpreted the situation, anyway.