I don't really look at it from what the company expects, but our interests are aligned here - we don't want the plane to be unsafe, so the end goal is to not let an unfit pilot fly an airplane. As long as that's accomplished, I'll do what I can to keep it between the other guy and me. For stuff that's cut and dry (alcohol, drugs, some health issue, etc), you’d just pull the other guy aside and tell him to bang in sick. You don’t screw around with it. If it were a recurring problem or there's evidence the pilot needs outside help, there are channels through the union to raise that flag in a discreet manner. Again, I'll never let an unfit pilot fly a plane, but I'm also not in the business of nuking anyone's career. That said, in almost 13 years of flying in a crew environment, I’ve never been put in that position.
Fatigue is tougher because it's a sliding scale, and it usually manifests itself in small ways - little mistakes, etc. At what point is it truly unfit? Obviously falling asleep and overflying an airport qualifies, but I've also flown after a crappy night's sleep, and while I wasn't having a hard time staying awake, I certainly wasn't 100% either. I'm not proud of it and I do everything in my power to be well rested before I fly, but I think most professionals that have done this gig for any length of time have been in a position where they're not exactly where they'd like to be from a fatigue standpoint. That's where my comment to your post comes from.