Answer: The defence of the case that the adjuster is using is an Insurance principle called "PROXIMITY CAUSE"
Explanation: Proximity cause is an insurance principle which states that a claim can only be fully paid if the cause of damage was not intentional, and the insured person or property was properly protected to avoid any damage. This explains further that claims cannot be fully paid or may never be paid, if the insured person neglect the risk of an event, and a claim comes up in the process of such event.
Since Sarah was playing a basketball on a stair case which has increased her chances of getting injured, she has willfully giving herself in, to be injured. That means she has not properly protected herself from injury, and therefore she has to pay some part of her hospital bill.