They correctly show that government debt did not cause the current crisis but total debt did. By stating that the increase in private sector debt caused it they almost (incorrectly) imply that therefore the private sector (and the people) are to blame. Of course it's the responsibility of the government to take corrective measures to ensure long term financial stability. The European governments were completely negligent in that regard. Note also that the financial sector is not mentioned at all in this analysis.
The nasty dilemma offered at the end is a false one. First the article observes that government spending was not the cause of the crisis, and then the solution revolves around government spending? The current eurozone debates are about politics: the people in western Europe want to punish the countries they see as irresponsible. That's why we have all the talk about austerity measures. Austerity will only further cripple the economies of the GIPS countries as we've seen during the Great Depression in the 30s. Austerity doesn't work: it leads to criminal levels of capital waste: high unemployment, low standards of living, poor liquidity, and so on.
So the question isn't "Should the GIPS countries spend money to prevent a worse recession?" the real question is "How can the GIPS countries get the money to prevent a crushing depression and a lost generation?". There are a number of options: ECB bailout. Eurobonds. Bailout by the richer part of the eurozone. Various forms of quantitative easing. Unfortunately this is difficult as long as the people in Europe are angry at the GIPS countries. No politician is going to support a bailout at the expense of the richer countries if the people want to see blood.