Flingingwings, i agree. whoever signs the auth sheet is PIC.
this is why, as an FI, if you let a student startup on his own, you are putting yourself/your licence at risk.
because he is flying the aircraft, and you are inside drinking tea, yet you are the legal PIC.
99.9% of the time its not a problem. but when he f*cks up the startup and chops the tail off and, heaven forbid, the debris kills someone, the CAA will be gunning for YOUR arse, as you were the legal PIC.