This is, IMHO, one of the thornier problems that has many, not often considered, implications.
Cap 371 says, as has been noted,
"
A Commander is authorised to exercise his discretion in the following circumstances and to the limits set."
Note "authorised" and not "entitled" or something stronger. Had the draftsman wanted to allow Captains to be able to put crews into discretion entirely at their own behest that would have been more emphatic. It is merely a permission that makes it lawful to extend the hours as per the rest of the paragraphs.
A Captain gains his authority as an aircraft commander from the company he works for, and no-one else. The fact that, by benefit of being an AOC holder, the companies award of that position carries with it certain legal responsibilities and powers does not change the fact it is a private company related post. If you have a situation where Cabin crew, for example, working agreements lay down stricter rules than CAP 371, the authorising granted by CAP 371 does not override the fact that your employer has agreed to work to lesser limits - that fetters your hands as a Captain. We do not, as Captains for whichever company, have the authority to over rule the CEO on contract matters - unless that authority has been specifically granted. Compare it, say, to the Alcohol position. were the law to say no drinking within 12 hours of flying and the company to say it is 24 hours, which one will, practically speaking, prevail? The position is that the most prohibitive of the 2 will be the one you must adhere to.
Flt Ops inspectors may have their views, but until they start appointing High Court Judges as Flt Ops Inspectors, FOI's are not in a position to give a legally accurate definition of the scope of any part of the law. As 411A said,
authority rules alone...not by committee.
and in this specific area, that authority does not lie within the CAA.
I would suggest Commanders be very circumspect indeed about trying to take other than a totally willing crew into discretion, for many reasons, including their liability resulting from their duty of care to both crew and passengers.