Jet 11
Unless you are able to give details of the defect, one would have to say that the Captain was probably right because it would have been his assesment, in the absence of an approved engineer, that the door was indeed u/s.
The door need not neccesarily have to be working in a convenient (to Cabin Crew) way for it to be properly operable in an emergency situation and, having had it reported to him, I am sure that the Captain would have taken these circumstances into consideration before taking the decision to go.
The combination of expediency and professionalism as practised by a Captain is a very fine line indeed, which is easy to occasionally misinterprate as dangerous by the misinformed or ignorant.
Shout "safety" and too many people duck for cover instead of being objective. It's called arse-covering in some circles.
oscar