I heard the same thing while at a regional airline. They only want you to continue, and expect you to be able to get 8 hours of sleep every time you are put off duty, regardless of the time of day or how much sleep you JUST had (like this guy). They look at the regulations and see you are legal, and forget that you are not a machine. In the time I was there, some guys were even threatened with termination in this situation. It improved immediately when we got the union in.
Safety is first. This driver told three guys that he is too tired to drive safely. All three of those dispatchers put money ahead of the driver's life (and everyone he passed on the road) and told him to continue. Heinous - especially since he told all of them he was starting to microsleep. Note how they try first to persuade him, then try to browbeat him into driving, then threaten him and his family before "letting" him get some sleep.
As the driver (pilot) you TELL the dispatcher you are too tired to continue safely. Their only correct answer is to tell you ok and get someone else while you rest.
The ironic thing about this situation is that it always happens when you're exhausted so you end up receiving persuasion from someone who is fresh and rested. And when dispatchers are invited for ride alongs, they invariably take them but only on cake runs in good weather.
I'm not saying there aren't people out there that abuse the system and call tired when they're not for whatever reason. There are.
Edit: watch the last minute of the video. They told him to sleep for two hours, then used the police to wake him up 45 minutes into his rest!!!