Even if you pay your credit cards in full before your payment is due, your credit report will still show you have debt. The only way for your credit report to show you have no debt is to pay off your balance in full the day before your billing cycle ends. That way your bill will show a zero balance.
So, I vote that if your credit report shows you have no debt, then I will agree with you that you have no debt.
However, I think the way some people are arguing, "the moment you swipe a card, you owe a debt" then you would also have to all your bills as debt as well. The moment you turn on that light switch you owe the electric company, the moment you own a house (even if paid off) you owe real estate taxes, etc. Unless you are prepaying for all those services, then no one could could ever be debt free by some of your definitions.