Bolded by me-
Giordano is still a suspect in this case, that is why he does not tell his story, it is not in his best interest and his lawyer would have advised him not to do so.
Imagine he would go tell the beach-snorkeling story, the story we have read over and over again, nothing new there if he would tell it again, but given the circumstances he was in, being on television, having his children stand behind him, the host in front of him who may interrupt him at any moment, having been in jail for 4 months, being fed up yet having the desire for people to believe him, there were a number of factors present that could have led to him saying something just to be liked better (like "yes I did look back" while he didn't) or because he was interrupted, or because he would want his sons to be proud of him.
There was a risk he would contradict himself and since he is still a suspect he cannot risk that, even if he would want to Baez would step in immediately. IMO