If he hadn't reported to the AP office he probably would have taken a taxi back to Kuwait a few days later and returned just the way he came.
Didn't anyone read the whole artical? He didn't get in through Kuwait as the boarder was closed. He flew to Baghdad from Beirut helped by family friends that he went to stay with after failing to get into Iraq on the Kuwait boarder. He phoned his parents from Kuwait to tell them what he was doing and thats how his presence became known to the authorities there.