I don’t Think the White house has a recent reputation for “truthfulness”.
They were probably ready to say “obama did not authorize Deadly force” if things had gone badly for the Captain.
Obama was ready to “bow” out on Bad news.
Let's be honest here. We won't know all the inside details until Vice President Biden decides to fill everyone in on how it really happened. Ole Joe will tell us all about it sooner or later, as only he can tell it.