According to the Congressional Budget Office there was a decrease in 2000/2001. According to the NPR story and the original graph you linked to there was a decrease at this time.
According to your CBO link, debt held by the public decreased. I'm not disputing this point. However, debt held by the public is only one component of federal debt.
The other kind of federal debt is intragovernmental debt; that is, debt which the federal government owes to itself. This category includes the Social Security Trust Fund.
And that does not really count. If government department A owes 10 dollars to government department B, the total net government debt does not change. So yequalsx's data is correct for the purposes of the present discussion.
If you borrow from your 401K, you're borrowing from yourself, and you eventually have to pay it back. It's money that you owe, to be paid with funds that can either be used to buy jelly beans or put back in your 401K.
If the government borrows from Social Security, it takes that money out of itself and spends it out in the economy. SS and the government has a smaller pile of cash, and the government owes itself. When the money is put back, it's with funds that could either be used to buy bullets or put back in SS.
Why does it not really count if you're actually paying back the social security trust fund? They can borrow from it, surely it also counts as debt. Just because you say it's going from department a to b doesn't mean there aren't real implications for that money being owed or not.
http://www.cbo.gov/budget/data/historical.pdf
According to the PDF there was a decrease in public debt for a number of years during the Clinton administration.
NOTE: I think the chart you linked to includes private debt and isn't just federal debt.