Counter example: No companies I've worked at had an explicit policy of rejecting a resume with a picture/photo. Whether it was done by some people in practice - unsure.
Edit: This would lead me to believe the law is somewhat up for interpretation and it's not cut and dried, since AA is a pretty big company and I would assume their legal dept had to sign off on this kind of thing. That being said, they are pretty well known for being sketchy and creepy.
American Apparel claims it hires "models" and not merely people with any skill in particular; that's how they get away with discrimination based on physical characteristics.