CAP 371 puts it like this (but of course it's what's in your own airline's FTL scheme that is guidance you operate to)
'An aircraft commander may, at his discretion, and after taking note of the
circumstances of other members of the crew, extend an FDP beyond that permitted in paragraph 13, Tables A, B, C, or paragraph 23, Table D, provided he is satisfied that the flight can be made safely.'
boredcounter, it would be less than CRM if a commmander took it upon himself to decide that his crew were fit for a duty off his own back without a bit of consultation and discussion.
You are of course correct though; Ops and Crewing's have no input into the actual decision to extend a duty. However, the information they give to the crew is important and must be realistic to base their decision on is.
There are occasions when Ops might just/should put a stop to a flight even though discretion has been agreed; on the basis that they may have no confidence that the flight can be completed within the extened FDP. I have seen this happen many times, particularly after diversions on a foggy morning where the crew want to get it back, ops want to get it back- but the delays that we all know about during bad weather can put you at risk of going beyond sensible discretion, i.e. over two hours in my view. Remeber also, that discretion that goes beyond two hours requires a report to the CAA giving the justification both by the pilot and the ops manager.