Any time you see this phrase in your writing, just stop, delete that sentence and try again. "The fact that" is about as essential to any sentence, as a towel to any trout. Still, less confident and less skilled authors continue to use it to try to make their writing sound more official and educated, to add extra weight to certain statements, and to camouflage faulty reasoning.
It is due to the fact that Britney Spears is the voice of a generation that she's sold millions of records.
The fact that people continue to smoke cigarettes despite the health risk stems from how much they love the taste of their particular brand.
The fact that men want to have sex more often than women is because men like sex more than women.
Yeah, right. Let's try something self-referencial.
While the phase "the face that" is gramatically correct, that doesn't change the fact that it should never be used.
Have I proven that this phrase should never be used? Nope. Instead I've asserted that it's is proven elsewhere... which of course (as Any points out below) it isn't. At one point, I had a lot more hand waving in here...
Suffice it to say, you may find places where it is not redundant or extraneous, when dicussing "a fact itself rather than the underlying reality". However, I think you will find those cases few and far between. And even when used correctly, "the fact that" sounds like lame joke to me. Every time I see it, I hear a drum set in my head.