Is it legal for schools to publish SAT scores to the student body...

Just looked this up. Didn’t go far in depth, but possible this is a FERPA violation. This sounds like something that should not be disclosed without parental consent:

http://www2.ed.gov/policy/gen/guid/ptac/pdf/slides.pdf

As an aside, maybe someone could use FERPA to stop the lousy practice of high schools putting test scores on transcripts!