Your theory is apparently shared by others:
http://www.homelandsecurityus.com/archives/6860
Note the speculation that the guy that made “the video” may have connections to DoJ.
There was an article or two by Walid Shoebat about this; the video maker (or whatever he is) was business partner with Shoebat’s cousin, a Palestinian jihadi. Very shady fellows. The Coptic Christian thing is no doubt a lie, Shoebat explains.