That's like saying "If you borrow money from your parents instead of a bank you're not in debt - it's just paperwork playing".
Debt is debt.
And furthermore, the official debt numbers don’t even include our essentially unlimited obligations we now have to Fannie Mae and Freddie Mac.
No, it's like saying 'I'm going to hit up the vacation coin jar for some money and leave a note to myself promising to pay it back.' It's not debt, there's no way to force a collection, and the government can waive that debt away any time they like.
The majority of that money is Social Security Trust funds, and that trust is no longer creating an excess - that money will be 'paid' back by us converting it from money the government owes itself to publicly held debt, since there's no way Congress is going to even attempt to balance the budget or bring costs under control.
In any event, the public held debt number is important for us to compare to the rest of the world as the sovereign debt crisis continues. Because if it really starts hammering the dollar (I'm not sure what it would be in favor of), it won't be long before Congress waves the magic hand, and makes that 4 trillion of inter-government debt disappear, and knowing this, you may be able to take advantage of the situation to gain some profit before the massive crash happens.