The same does not hold for Eurozone governments, hence the debt crisis. In fact, Eurozone governments are more akin to US state governments, and the debt-to-GDP ratios of US states are much lower than those of Eurozone members. The debt crisis should not have been a surprise to anyone, and the fact that it was shows how little the monetary system is understood even by most economists.
That said, I disagree with the last statement made in the article. There is in fact a very good reason for governments to go into debt at least under current institutional arrangements. (Monetarily sovereign) government debt is just another form of money, and in fact money is a debt of the government (via the central bank, which is really just a branch of the executive when push comes to shove). And the private sector really likes holding on to money.
Private entities that are economically successful like to collect those shiny numbers in their bank accounts, and hence they accumulate monetary assets without spending them. They have lots of income, but spend only a part of that income. This means they effectively act as a money sink. The money that is kept out of circulation needs to be refilled somehow, and government is the only entity that can do so.
So there are really three options: 1) Accept that, under current institutional arrangements, the private sector accumulating monetary assets means that the government has to go into debt; and accept that this is not a bad thing.
2) Change the institutional arrangement so that the government can just finance its deficit by creating money outright (and use taxes to control inflation).
3) Raise taxes on wealth to the extent that the accumulation of assets in the private sector simply is not possible anymore.
Personally, I believe 1) and 2) are the best options. 2) has the added benefits that it eliminates interest payments by the government; I consider this a benefit, because those interest payments tend to be a hidden subsidy of the rich.