It might be useful to spread such a rumor in the Arab world- that that's exactly what we're doing. If they believe our soldier's sunglasses allow us to see through women's clothing, they'd probably believe it.
On a side note, I'm thinking about that bug the agents put into Neo's belly in the Matrix. We're not so far away from that, really, and your idea is basically the same thing.
RE: spreading rumors....We don't want them to know about the tracking and timed poison devices when we do prisoner exchanges, but we would want to deter prison escapes. It depends which we care about more. I'd prefer to keep it secret.