A pitch adjuster is software that allows the user to change the pitch and timbre of any recorded sound. So they took the recording of Obama's speech, spliced together the sections they wanted, then ran it though a pitch adjuster to create the melody. Then they synced the pitch adjusted recording with the parts of the video where he actually spoke those words, and viola!
So it is actually what they said, just in a different order and at a different pitch.
(this is also how bad singers get to sound like good singers)