Sorry to be late in replying.
I’ll answer by putting it another way. If a private person offered to take it in their own car, or a Rep that was going that way, or a Taxi driver with a regular Airport contract, was to do the same, what would their position be?
For any claim to be successful, the claimant would need to establish Negligence. Simply that the goods were damaged/lost whilst in the custody of another person is not sufficient. It would require evidence that the person transporting the goods understood any risk associated with their actions and deliberately chose to ignore those risks. For example, leaving the vehicle unlocked, or parked in a secluded location, whilst at an MSA.
Having the vehicle broken into when parked at a high pedestrian volume location would not normally be considered Negligent, although I could name a few locations where even visiting that area would be almost negligent. 
I do not see that GIT insurance would apply, and my attitude, if put in that position would be, “So, sue me.”
Hope that helps.