This emergency authority comes from a level higher than the company....higher than the authority that gives the company its AOC.
This is enshrined in international as well as national law.If a Captain uses this authority and gets it badly wrong...or (other side of the coin) an F/O were to contravine this authority and hull loss or similar occured you can expect to be looking down the barrel of a jail term.
It is normally a good thing for an F/O to know the routine SOPs inside out and advocate correct adherence.
On the other hand if you have an extreme emergency and the skipper uses his experience/ local knowledge etc (which is what he is really paid for) there is not likely to be time to debate it. The stats show that whilst these kind of immediate decisions may be less than perfect... the outcomes are more often than not ultimately satisfactory.
There is a whole load of science behind this (search schemers) etc which proves the experience debate.
The mistake that is often made (at the risk of insulting intelligence) is that because he cant use the FMC as well as you / knows the exact words your company likes to use he will get it wrong when the book has to go out of the window. As an F/O with a Captain who has become incompetent through age / attitude or should never have been promoted in the first place this becomes difficult. It can normally be managed but its a tough one.