Did the person have the required amount to enter. I have never been asked to prove I have enough money but as an Australian they can refuse me if I have less than AUD$2000 in cash.
I can only talk about Australia. My wife is a Permanent Resident and can reenter for 5 years after the grant, after that she needs a reentry visa. For $500 of course.
They started by refusing to give reentry visas to people seen as undesirable.