The goal of the bailouts is to minimize the effects of bank failures on the economy, not to make sure the banking system is sound in the future. The counterexample isn't valid. A valid counterexample would involve a country avoiding a recession while not bailing out failing banks, but even then, I don't think this particular situation has a historical precedent similar enough to be pertinent.
Also, after actually looking into the example, it looks like Sweden did bail out the banks to end the crisis: "The government rescued the banking system by issuing a general guarantee of bank obligations. The total direct cost to the taxpayer of the salvage has been estimated at around 2 per cent of GDP." (http://ideas.repec.org/a/oup/oxford/v15y1999i3p80-97.html)
Even with a valid counterexample, I think you should still have to explain why the current course of action is wrong, not just why another would be right, which is why I didn't address it in the first place.
Also, after actually looking into the example, it looks like Sweden did bail out the banks to end the crisis: "The government rescued the banking system by issuing a general guarantee of bank obligations. The total direct cost to the taxpayer of the salvage has been estimated at around 2 per cent of GDP." (http://ideas.repec.org/a/oup/oxford/v15y1999i3p80-97.html)
Even with a valid counterexample, I think you should still have to explain why the current course of action is wrong, not just why another would be right, which is why I didn't address it in the first place.