Could a 172 have handled it? Of course, no problem. Would the NTSB have blamed you if it had gone down? 100%.

The benefit of being the PIC is you get to make the final call. You can get grilled for not being a 'team player', making the school look bad, cancelling flights, and turning off clients. But it's your certificate on the line, not your boss's. If the PIC says no, it's a no. Period.