The reason why he knows about all these deaths is because he actually IS Death. The whole show is actually him recounting some of the weirdest, dumbest, or most entertaining deaths he has witnessed during his career. Like most portrayals of him, he's not a bad guy at all and is just doing his job, albeit with his own twisted sense of humor. That's why he condemns the actions of all the bad people who have died, and discourages listeners from being reckless and stupid like the victims in his narratives.
WMG / 1000 Ways to Die
The Narrator is The Grim Reaper himself