Unlike what this article suggests, tax fraud is also relatively common (one would have to be rather daft to assume that a country with such absurdly high taxation did not have tax evasion as a key pastime - although probably not as aggressively as in places like the US), and while heavily frowned upon certainly not seen as the highest form of crime as this article suggests. Well, maybe if you ask the tax agency and the political parties pushing for ever more welfare, both of which push heavily for a cashless society where all financial transactions are fully trackable by them, but I think most would place tax evasion quite far down on the list of significant crimes.
I would instead say that the average Dane is carefree about these issues, not because they are trusting or believe their system is worth religious following, but because the issues experienced there feels quite minor compared to what seems to happen elsewhere in the world. When your concept of a significant natural disaster is a flooded basement, you tend to not worry that much about what happens locally.