I agree with it being pretty impossible nobody caught this error in 10 years pretty much giving it away that it's not a real error. However, it's a real hundred dollar bill, just not sure how they made a photo copy of a 20 on it.
Definitely overprinted AFTER it left the BEP. The note was printed in September 2013, and possibly just overprinted a month ago. So the notion that no one spotted it for X amount of years doesn't hold up.
Interesting, but I'm not a big fan faux errors. I'm certain it hurts the hobby we all enjoy.