The other red herring in this, is if the aircraft is utilised at a training school.
ALL of the schools I have flown with have insisted that for training flights, the MR shall be signed by an instructor.
I have seen it many times, where the aircraft has been signed out and flown by a PPL/CPL, and the MR is then re-signed for the subsequent training flights by instructors.
I'd assume this is more insurance/Ops Manual dictated?