if i were you (being a law student) i'd get them to write up a written contract for you to sign which would be legally binding, so you can see everything in writing and be able to know exactly what the situation is. i personally would NEVER rely on something that's been said over the phone.. (made that mistake today... and almost cost a company £8,000 [the fact their turn over is £4billion a year doesn't make any difference to me])
it does seem to look rather legit but at the end of the day only go ahead if you are feeling comfortable, and hey i can see why they like your image.. just looked at your profile pic :P