However, it is clear that the strategy has a cost in terms of credibility. From the New York Times this morning:
But the shifting narrative may have distracted from the accomplishments of the Seal team and raised suspicions, particularly in the Arab world, that the United States might be trying to conceal some of the facts of the operation, including that Bin Laden was unarmed.
“It’s had a hugely negative impact,” said Ahmed Rashid, a journalist and author who is an expert on the Taliban and radical Islamism. (...)
“Liberal Muslims who are very sympathetic to the death of Bin Laden really don’t know what to think,” he said. “The American story is very confused.”
From Europe, even the archbishop of Canterbury weighed in. At a news briefing on Thursday, the Most Rev. Rowan Williams said that the killing of an unarmed man left him “uncomfortable” and that “the different versions of events that have emerged in recent days have not done a great deal to help.”
So the strategy depends, in part, on the relative benefit and cost at stakes(ok, that's obvious). What is interesting for me here is that the credibility costs seem to be huge: the domestic audience is prone to believe in conspiracy theories, and the US suffers a huge credibility deficit, notably in Pakistan, where the legitimacy of cross-border strikes from Afghanistan is a matter of debate, and each drone strike leads to some damage containment by the Pakistani government.