While it is a forum I was looking at, I don't see why it's any less reliable that this one. Indeed, the fact that it is a fairly large forum devoted to aviation (and specifically commercial aviation), would suggest that, were fabrications brought up, they would probably be pointed out and shot down in flames pretty quickly by other members. The claim they make about Sudan is
not that fly overs are forbidden, but that no US airlines fly there (and the implication inferred from this is that the Sudanese government is probably not willing to give regulatory approval to said US airlines). They point out that airlines from non-US countries regularly fly there, by
posting a link (admittedly to a blog) in the second post on Sudan.
In terms of Zimbabwe being anything other than a complete basket case... well... I guess I'll just have to believe almost every commentator in the Western world on this one. But to look at two fairly reputable sources, the CIA World Factbook points out that "the government's land reform program, characterized by chaos and violence, has badly damaged the commercial farming sector" and later that the Zimbabwean dollar's official exchange rate went from 162 per US$ in 2006, to 30,000 per US$ in 2007 (with a realistic unofficial figure of 800,000 per US$) - which, by my calculations, is 493,800% inflation. Meanwhile, the BBC country profile describes how "the forced seizure of almost all white-owned commercial farms, with the stated aim of benefiting landless black Zimbabweans, led to sharp falls in production and precipitated the collapse of the agriculture-based economy". The considerable international sanctions against Zimbabwe would suggest that he is annoying more than just his own people.
Anyhow, I digress, while it is certainly true that fly overs are a source of good money (as that forum suggests RE North Korea), to many of these dictatorships, the hatred of the West, or more often certain countries (like the US or UK) for various reasons (such as a belief that they are trying to impose imperialistic policies on them) leads them to be quite willing to ostracise those specific countries, even if it means they lose a little money. The fact that these dictatorships often have huge sanctions imposed on them by foreign powers would suggest that acquiring foreign currency is probably not their primary goal - but rather, their goal is satisfying the strange whims of their dictator - even if that means turning away a few British or American planes.
But in the end, even if the worst parts of Africa are perfectly safe, successful states, the perception in the west, as pointed out, is that they are dangerous, which would make it quite plausible that rich 777 owners would divert around them - regardless of whether the fears motivating them were true or not.