There are times when the captain is required to make decisions that are unpopular with the airline. Some of the reasons may appear trivial, but if the decisions are made in good faith there should be no significant action taken.
If the Operation Director or other management staff are so intent on taking away such decisions from the captain, they should fly all the flights.
There are some captain decisions that traditionally suffer little or no management interference, like go-arounds and weather avoidance. Where management feel, correctly or not, that the captain is disrespectful of them or unconcerned about profit and disruption, they are more inclined to interfere severely in those areas.
Pilot retaining his authority to accept MEL items or not, is an area where I have seen airlines more inclined to try to deny the captain his considered choice. Finally, the public statement avoids mention of the captain's multiple considerations.
The process is more difficult in some cultures, with a foreign contract captain or if the co-pilot decides that MEL acceptance is not sufficiently safe.
Often the acceptance decision is reasonably clear cut, and even in the face of company pressure, there is little lasting action. The more difficult situation is where a decision is counter to normally accepted practice.
In spite of the difficulties, the captain is bound to make the most correct decision without fear or favour.