RE: Jindal was born in the U.S. to parents who had green cards at the time via his father’s profession.
Where did you get that piece of news?
His mother came via student visa, which means his father came here as the spouse of someone with a student visa.
Eventually they secured green cards, but that was AFTER he was born.
See here:
http://freakoutnation.com/2010/08/03/bobby-jindal-was-an-anchor-baby/comment-page-1/
http://www.nola.com/politics/index.ssf/2011/05/gov_bobby_jindal_releases_his.html