Typical fallacy in entropy considerations is to consider system as isolated in the model while it is strongly connected to the environment in reality. The oil/vinegar (similar to the pennies and dimes mentioned in the article - when shaken in a jar would "magically" separate with pennies on top) has exported the entropy to the environment through the work of gravitational force in full accordance with the 2nd law - the system transitions following the gradient and thus increasing total entropy of the whole system. A similar mistake for example is when "life" is stated to be "anti-entropic" in any sense while it is a really a form of matter organization which generates even more entropy than the same amount of dead matter would.