Much depends I should imagine on the Terms and Conditions of Contract between the airline operator and the handling agents. Contracts and the price paid between various agents and operators will vary throughout the industry similar to many other businesses that have "contracts".
Swissport may have more liability for example with any other operator than what they have with FlyGlobespan. It depends on what has been negotiated and indeed could even possibly vary between airports served by the same airline with the same handling agent. Its all in the beauty of negotiation, value for money, risk assessment and liability.
Nivsy