Did you actually read the article this time?
First off, Steiner is a layperson and his analysis is overly simplistic as a result; relying only on looking at the Treasure website. In essence, he's engaging in straight cash accounting. He's essentially relying on the difference between the CBO analysis (which factcheck gives) and the Tresury's ledger number (which is what your source gives). This allows him to double-count all debt that the government owes to itself.
Your source goes out of his way to state that Clinton did pay down the public debt. The reason the cash accounting numbers make it appear the debt got larger is because the Social Security Administration purchased US Treasury securities. Thus, your source is actually engaging in the accounting trick, rather than the other way around. He gets to count excess money that was not spent as "debt" because it was used to buy US Treasury securities.
If you read the article, he's not even hiding the ball on the stunt.
Factcheck, and the CBO estimates it relies upon, on the other hand correctly calculate that not as full debt but as intra-governmental debt that is properly valued for its long term debt consequences only at the expected value of the yield on the securities. The principal value effectively doesn't matter because that is money the government owes to itself.
Factcheck went out of its way to dispel the social security as accounting trick argument:
Where did candrew play the card?