As the guidance states, the bank is ultimately responsible for that 3rd party's compliance with the banks CIP.
It is permitted in relation to a loan, as you stated. What regulator is this? I would bring your FFIEC guidance with you and ask him where it says anything different. We have car dealers that we rely on to obtain CIP. But, we also perform non-documentary verification on our end.
My opinion is mine only- not my employer's!