You can get candid shots in a studio session...
and
I think what they may have been looking for is natural shots. Not the "cheese" smiles. Its unfortunate that the parents got in your way. I picked up a trick from a seminar and it was to give the parents a refelector and tell them that you need help with y our lighting. Make sure the reflector is held over their face and far enough from the subjext to NOT distract you. I've only had to do this once...