HFD while I agree in the principle of who does the check....
Its really the flight training industry's fault that this situation has occurred. Inexperienced FI's who change every 6months to a year, bitter and twisted CFI knob jockeys. Its no surprise that the majority of owners and groups actively avoid any flying school and the associated politics.
If there was a financial risk to none FI/CRI's doing the checks the insurance industry would have stopped the practise years ago. They haven't and there is no legislation to stop the practise. In fact I seen quite a few insurance policy's with named PPL's as the group check pilots.