I am not a lawyer but let's say that a renter (or the lawyer representing his estate) is able to convince a court that the renter could not have reasonably known that the CofA had lapsed. Then the owner/operator (the school?) will go down for the passenger liability.
In my renting days, no renter ever checked any of the aircraft paperwork.
By virtue of Part 21 an EASA aircraft is obliged to carry its C of A or permit on every flight.
Under the provisions of Article 86 of the ANO a non-EASA private aircraft is required to carry its national certificate/permit on any international flight (Schedule 10(2)).
Article 52(c) of the ANO requires the commander of an aircraft to take all reasonable steps before flight to satisfy himself that the aircraft is in every way fit for flight.
It would be hard to imagine a scenario where you could convince a court that a renter could not have reasonably known that the C of A had expired because it would beg the question what reasonable steps had been taken to satisfy himself that the aircraft was fit for flight? If the paperwork is not available/the pilot failed to look at it how could it be said that all reasonable steps were taken and he/she was properly satisfied?