The advice I received in a similar situation was to do an IR test from the earth to the exposed metal. I can't remember the limits, but if the value is sufficiently high I don't believe it needs to be earthed.
I asked because I was doing an EICR and could find no earth continuity between the RFC CPC and the exposed metalwork of the fridge/freezer, but there was continuity to the compressor cradle at the rear of the unit.