There was a discussion on whether George Martin should get songwriting credits for Yesterday, last year. We also discussed the matter in the Fifth Beatles section: http://www.dmbeatles.com/forums/m-1140552856/
George Martin arranged the string section. To the best of my knowledge, he didn't have a hand in writing the song (Please correct me if I'm wrong). Someone who arranges a string section wouldn't get songwriting credit because the song structure, in it's entirety, must exist before the string arrangement can exist. The string arrangement, (or guitar solo, or sax solo, or keyboard part) is entirely dependent on the song, which is why the contributers of such do not automatically get song writing credit. They contribute, and their contribution is noted elsewhere, but well think of it like this: If Paul played 'Yesterday' live in concert, accompanied by just his guitar, minus the strings, would you still expect to see George Martin's name on it?
The answer would be no. Because George Martin didn't write the song, he arranged the string section.