While I personally prefer not to use fill flash, that's the primary reason flash is used in sunny daylight - to fill in the shadow areas of the bird - especially shooting in the early afternoon where light is coming down from above, so areas like underwing and tail, and under the bill, can be in shadow. Also, the flash provides a 'catchlight' - that little glint in the eye that gives it some dimensionality and life as opposed to it being a dark orb.
It's all in the photographer's preferences - if looking to document birds to see their every detail and pattern, the flash can be useful in making sure details aren't lost or obscured to shadow. If looking for those 'Audubon' type shots, where the bird is perfectly illuminated like a drawing, it can be useful as well. Other photographers might actually prefer the real-life type look of the bird, shadows and all, as that provides a fully realistic setting and lighting situation as it was spotted on scene - personally I like the way shadows can add drama and reality, and a fleetingness, to the bird image, so I prefer to let my shadows be and never use flash. Neither is a wrong way to do it - all in the photographer's personal taste and desire!
