I had first tried to see if there was a White House page with the picture but had no luck. Apparently the WH is not sufficiently proud of the shot to put it in its own site.
I would assume that the WH has professional official photographers, as does the Air Force. Is there a possibility that this photo was taken by a satellite?
It's important to use the actual file if you want to look for metadata.
In that file you will find the EXIF header has been removed, so we don't know what type of camera was used. My guess is it was the pilot's personal $150 point-and shoot and he took this picture as a souvenir. There was no professional photographer on the F-16, as the intention was to film the two planes together from a thrid platform.
Also, you can tell the file as been photoshopped (maybe just to remove the EXIF data) by the distinctive presence of tags "JFIF", "Ducky", and "Adobe" in the header. Google those tags to see why that is a signature of Photoshop.