In my hardly humble opinion, the captain is responsible for the welfare of all the crew.
Therefore, if someone turns up sick (unfit) the captain has a duty to call crewing and require a standby to be provided. Obviously this might not work too easily at the start of a four sector early. But it should be feasible at the end of the second sector, assuming return to a company base before launching on the third sortie and assuming that the crew member is still alive to be relieved.
Furthermore and depending on the type of aircraft; I have always considered that a captain should have in mind the physical needs of his crew, for hot meals, loo breaks and so on, before entering into discretion.
Captains are usually in fairly short supply and are not so easily replaced as useless cannon fodder. They owe it to their crews to stand up to Crewing/Management in an effort to smooth and improve the quality of life for all concerned.
