If the images in the article are accurate, the birds don't really see the polarity of the field, merely the alignment, so they don't really see "north", "east", "south" and "west", merely "latitudinal" or "longitudinal".
They would probably combine with sunlight to get the real orientation – an approach which would continue to work with a flipped magnetic field.
If you have 3D polarized glasses from the cinema you can go outside on a sunny day see this alignment in the sky. It's really cool, highly recommended.
They would probably combine with sunlight to get the real orientation – an approach which would continue to work with a flipped magnetic field.