Ahh ... it's not THAT simple.
The PIC must have an overwhelming reason to reject a permissible unserviceability. That is, when they say no when presented the logbook ... pass them the phone, Duty Captain on the other end of the line. Short conversation later and he will be back in his l/h seat.
Many moons ago, some Qf captains took great delight in not accepting defects covered by the MEL. APU inop .. I'm not going .. yes, of course Captain.
Airlines stand to lose alot of doe when planes are grounded. If she's airworthy, she flies.