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.
Feel free to flame me, but every flying school/club has an Ops manual (copy lodged with CAA??) and an authorisation process.
The Ops Manual at the school I worked at had a pre flight document checklist, which included all the airworthiness and insurance documents (as well as many others). When the PIC signed the auth slips/sheets he/she signed a statement to the effect that they are fully conversant with the Ops Manual (signature sheet and amendments up to date) and have carried out all the relevant checks and pre flight requirements.
PIC carries the responsibility into the air. If the school/club is operating correctly case closed.