In theory, it checks out. But who knows if the FEDS accounting is legit. FED has basically issued no-recourse loans on junk paper valued at AAA. Which, yes, expands M3 by that amount. Which is why all the inflation hawks like me keep on about inflation. They're not taking any money out of the system. Socialized losses.
By the way, you might want to research who actually owns the Federal Reserve System to begin with. Those are the chaps who are really pulling the levers. Ben is a figure-head of power. Just a functionary.
Bernackes not dense. He's an employee. He knows it. So do his employers. Its a charade for the public to make it seem Bernackes got control.