Hey Baba,
Of course. But that would be too difficult to grasp for those who won't believe much of anything put out by the US. Just the usual rush to judgement based on some initial reports that often change as the days go by and new evidence comes in.
And can you imagine if the raid had gone badly or been a complete failure similar to Carter's bungled attempt in Iran years ago.. The damage to Obama and the US would have been absolutely disastrous and long lasting. Obama took a helluva chance, the reverberations of which pro and con will start to unfold sooner or later. The talk-show right wingers will certainly take care of the con part here in the US.
Hundreds of people are involved in situations like this. For the US to deliberately lie about events would, indeed, be a very risky way to go.