Yeah somehow the idea that bandaged-head due is the real Big Boss (the way he talks and what he does doesn't at all resemble what Big Boss would do) is kinda iffy.
It seems to make more sense that they wanted a new Big Boss on their side, so they made a fake one, because the current one was likely going to die or go crazy/evil/whatever, Cypher just wanted another on their side to control their army (ultimate commander/perfect soldier thingy a la MPO).
So maybe the big lie is that they even managed to make Big Boss think he's not the real one, if so they would have convinced everyone.
But any way this goes, MGS4 doesn't make any sense anymore. I'm fine with that.