They fixed it in the mix:
“The Obama inauguration performance was pre-recorded, as we learned a few days after the event. Here is how the live performance might have actually sounded, for all we know… This is a satirical hypothetical document, not an actual record of what happened on inauguration day. Albeit with a nod to StSanders, numerous viewers have also pointed out that the duration of this video (4’33”) makes it a sort of John Cage tribute.”
via Lucas at WFMU.