OP's report is third-hand, but as OP reports what the relative says the BA agent said at the counter, "the PriceLine ticket could not be verified" was the reason for not checking the relative in (and thus the deadline passing).

This sounds as though the counter agent did undertake the likely minimum required, e.g. to verify that the e-ticket number presented, did exist. Apparently it did not. Why it did not is most likely because PL had not yet issued it, but that is speculation.

Nothing in OP's posts suggests that the BA agent undertook any sort of evaluation of the relative's underlying motivations in purchasing a second ticket and whether the relative truly intended to depart Israel as that second ticket was intended to demonstrate.

Presuming that the relative's ticket carried heavy change fees, BA did the relative quite well by rebooking without fees.