Like Big Mick, I think it's exceedingly unlikely the beheading was orchestrated by the US. Those who ordered it would need an operative who could convincingly be mistaken for a known Arab terrorist, who was willing to cut another man's head off with a knife, and whom they could trust to maintain complete secrecy about it afterward. Quite apart from how dirty they're willing to get, would they gamble their careers on such a person, if they didn't have to? This is quite a trick to be pulling out of their asses, and it could easily backfire on them.