If the media ever caught wind of rampant murder occurring within the dungeon, the damage inflicted on the organization from such a scandal would have been far more damaging than killing staff members at random.
But since the author is only interested in drawing tits, this plot hook is completely wasted.
Wouldn't the rule about not leaving the country without permission be common knowledge if it applied to all explorers? Or if it's a lie, he should have used the card and not tell anyone, if it was such a valuable skill.