Sweden also trusted the public, they had many times more deaths than the surrounding countries (Finland, Norway, Denmark), and closer to mainland Europe.
You simply can't compare countries. Some countries have different levels of trust of their governments, different customs, different densities, different borders, etc... Most of Denmark by population is a small island, and by their culture, people tend to keep their distances. It is also a rather rich, homogenous country with a good welfare program. The policy to "trust the public with hard truths" may (or may not) be good for Danemark, maybe not for another country.
I live in France. We are not Danes. We don't trust our government, and anything is ground for protests. We can also panic, I noticed it first hand. So we have a part of the population panic buying toilet paper while the other part is protesting, and while I don't particularly like our government, I kind of sympathize with them, we are not making it an easy task. Ah and we are famously anti-vax too. We are also a well connected country, at the center of western Europe, so of course we have more cases, and I don't thing "telling the hard truth" would have changed anything. We do have a decent welfare system though.
So, I'd like to say that "trusting the people" is a good strategy, but really, it depends on the people in question, and many other factors. Every country is doing its best with what it has, even if it doesn't look like it, and we can't generalize.