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Just because there are mottes and baileys, doesn't mean the baileys are wrong; they may just be less defensible in everyday non-ideal speech situations.
Some examples would help here. If a common motte is the best argument for a bailey, that IS some evidence that the bailey is wrong (or at least unsupportable in the application being promoted). When a bailey is actually true, there are better ways to show it - in those cases they ARE in the motte.