It doesn't work that way... James Blunt and his own management get to make that decision. His record company only owns the recording of the song, not the actual words or music.Al would most likely not release it, if the artist denied permission. But, what if the "record company" denied permission. Blunt might have told Al he could release it, while his "record company" denied permission. As the problem with releasing the album was due to "record company politics". This would be my best guess.
Of course, the record company could be pressuring Mr Blunt into denying permission, but they would have to be pretty stupid to do that, since he'd be one of their most important artists at the moment.
And regarding the website that had to take down the parody, it may have been that they had ripped the instrumental from the original recording of the song and used that as the background for the parody. Either that or a journalist somewhere actually made a mistake...