Yes, the "taken out of context" claim is often a way to deny you said something. But in this case, it couldn't be clearer. FOX "News" took Vice President Biden completely out of context to make it look like he said that "the fundamentals of the economy are strong." The fact is, he was plainly quoting John McCain, and deriding him for it.
What's worse, the clip was presented as though it was from a recent speech, when it very clearly was not. No wonder they got busted for it, the clip was memorable from the campaign. But that never stopped FOX "News."