The question isn't really why he still has his job, the question is why hasn't anyone killed him yet. The answer was given years ago as the punchline to another excellent cartoon in which Dilbert tells Dogbert " Lately the only thing keeping me from being a serial killer is my distaste for manual labor "
The real question in my mind is why the PHB would think anyone would pay attention to his tweets.
@ina
I'm in the UK, too (and I even remember Hislop talking about his alter ego on Twitter).. AIUI, there's no law against impersonation unless you're trying to con people; but I wasn't thinking about that, more company internal disciplinary procedures: Carol might think she has power over the PHB in masquerading as him when she tweets, but because she can't prove he asked her to set up the account, it'll look really dodgy if she starts making him look bad (and even dodgier to regular Dilbert-watchers if she makes him look good)