Well when you have some stomach or your pants are well tailored then it is easier to use gravity to tuck a shirt back in than to undo a belt and align everything back up. He was sitting on bed and he removed microphone pack causing the shirt to be pulled out simple really.
Cohen and the crew burst into room screaming Borat stuff and then the Borat exits.
He has detailed his side of the story, as well as I hear in between writing the above that the girl is 24 and the 15 y/old thing is just Cohen doing character. Not to mention it all was documented by Guiliani in July and his story is the same as then with him just defending his position of no impropriety.
At the end of the day it has been blown up as a distraction for both sides and as you can see we both have occupied at least a few minutes with this. I'm not sure how much is distraction and how much is promotion for the show but clearly there's nothing to see here really.