This is, in fact, rather close to what I think is going on

Why is it so far-fetched that somebody could have been recruited to do a bin Laden impression?

Modern secular Westerners have got to get over the idea that they are smarter than everybody else, as though nobody in the entire Muslim world would be capable of doing what Rich Little and thousands of other impressionists have done for a living. It leaves us unprepared for meeting clever people, whether they live in previous ages or in other cultures. And it leaves them wholly unable to deal with wisdom. We start thinking that our ability to make blenders makes us 2000 years smarter than the apostles and makes us invulnerable to clever people with box cutters.