The way that web site describes the fallacy fallacy they're only admitting that someone can argue for something that is correct in spite of the fallacies they employ.
Not all fallacies are poor arguments, however. Many arguments that might technically be classified as fallacies can nevertheless lend substantial weight to a particular position, even if they aren't air tight arguments.
Take for instance the genetic fallacy. I often want to know the source of a piece of information. The fact that a story comes from, say, Fox News, doesn't in and of itself make the story wrong, but it certainly increases my doubts about it. When someone warns me that something someone else told me came from Fox News, I'm not going to disregard that person for employing the genetic fallacy, I'll be happy for their warning.
Appeals to emotion are necessary in many arguments, even if they can be classified as a form of fallacy. There's certainly reason to be suspicious when appeal to emotion is overdone, when you can't find any factual substance to go with the emotional content of an argument, or when you discover emotions are being cynically played upon. On the other hand, however, good persuasive rhetoric requires recognizing that human beings aren't analytical robots. If you abandon emotional appeals completely, based on some misguided desire to avoid fallacy, you'll cripple your ability to connect with most people.
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