This actually sounds more believable- if he had given them authorization ONCE why did he need to give it AGAIN?
My guess is they had to ASK PERMISSION before they fired, and had to wait around for a reponse.
So they asked, it took too long, the missed the opportunity, and when another opportunity came they HAD TO ASK AGAIN
I’m not up on military protocol, but in a situation like this, wouldn’t you expect the President to initiate the order rather than sit around waiting to be asked? The Navy was pretty busy during this time, while he was sitting around eating pizza.