It's mostly marketing. Danes, and other Scandinavians, love the idea that they are more honest then others. It's not correct in Denmark. I find Denmark to be a quite corrupt country
Tax-evasion in small scale called "sort arbejde" is quite common.
Former primeminister and current foreign miniater Lars Løkke Rasmussen is a interessant figure. He's famous for not even being able to pay for his own underware.
It's still a great country, just take the marketing with a hint of salt - a self certain smugness / hubris can easily make you blind to real problems.