The flaw isn't so much that they trust those sources, because then which sources can they trust at all? The problem is that they treat all sources equally, and that once a few non-reputable sources cite something as fact, it will be hard to remove the entry from Wikipedia even if a few other, more reputable sources, gainsay the same. The 'rules' of Wikipedia are such that if you can get some consensus, even if that consensus is among a minority of disreputable sources, then you have a claim to the truth even if the entire world outside that consensus loudly proclaims the opposite.

And, if some idiot Wikipedia admin (but perhaps I'm repeating myself here) decides to stake his reputation on this falsehood, you are fucked. The falsehood may as well be written in stone at that point, as far as Wikipedia is concerned (cf Jimmy Wales birthday).