No he didn't,
Djokovic 10,800 points
Nadal 11,330 points.
I believe that the reason the ITF declared Djokovic World Champion was because he gained more points in ITF events i.e slams, wtf and Davis cup
Djokovic earned 6,020 points in slams and wtf
Nadal earned 5,000 points in slams and wtf.
I have not counted Davis Cup for either, because the number of points won were inconsequential.
IMO anyone who watched tennis in 2013 could clearly see that over the whole year Nadal was the better player. At the year end,
Djokovic had 12,260 points
Nadal had 13,030 points