I didn't read the whole article; however, I've studied the same issue. Clinton's claim was touted in general terms as a "reduction to the deficit". This was media bait and switch. Bill Clinton reduced the deficit of the annual budget. So each year's budget required less debt funding than the previous year. Pretty sleazy advertising, right?
He didn't reduce our overall deficit at all - in fact, he increased it every year overall. Additionally, just like Massachusetts liberals claim about Romney, Bill Clinton left a huge structural debt. IOW He put off a lot of necessary maintenance for the next president to deal with, reduced our military to a level that is too low (many say that it led to 9/11), and signed the fair housing stuff.