I always suspected it’d be Bert rather than Ernie.
In searching Bert and Ernie online for my daughter (she’s a big fan) I found this. Apparently a guy did a bunch of photoshopped pictures of Bert for a joke site, and this was among them:
But then somehow a bunch of Bin Laden supporters ended up with that picture on their sign (look closely at the bottom right). No-one seems to know how, but it’s darn funny.