MMmmm very interesting but back to the original question ....
"why did the Tech Mngr refuse maintenance action"? and give NO REASON!
If the failure to reach minimum power specification was written up in the A/C tech log or maintenance release THEN it effectively grounds the aircraft untill it is cleared by a suitably licenced engineer/mechanic. In clearing the defect he will have to justify in what way that defect is allowable IAW the responsible Regulatory Authority, or the Approved Aircraft Maintenance documentation or procedures.
If as a pilot you are not happy with that then do not accept the A/C and involve your Chief Pilot.
BUT DO CYA (Cover Your Arse) if it turns to !!!! the paper trail will hopefully absolve you and allow your kin to sue the Tech Manager and the Company that resolved to perhaps direct (force?) you to fly an A/C of questionable serviceability.