They don't consider the government some hateful opponent entity (or rather, they don't consider the state that. They can still hate this or that particular party / person running the government, protest its decisions, etc.).
The government is people they have voted into power to pass laws and guide the state machinery. They expect from the state to promote arts and fund culture, the same way they expect of it to make roads and maintain public infrastructure.
The US doesn't need that because
(a) there's not an emphasis on culture in the European sense, it's more about entertainment, most don't even believe there's a distinction between these two
(b) it dominates globally and has the most money, so they can push their culture everywhere anyway and teach global audiences to prefer their ware from a young age (after enough Spielberg and Michael Bay and superhero stuff kids become desensitized to movies with no SFX and explosions -- that happened to European cinema -- once equally or more popular as the American in Europe -- after the late 80s and the rise of the Spielberg era),
(c) it still gives all kinds of incentives, tax breaks, government (e.g. army) support for movies anyway, just doesn't call it for what it is
Various states, notably Georgia, provide tax breaks and other incentives to lure studios into filming in their jurisdiction.
In some cases it's a region within a country, such as Yorkshire: http://www.creativeeuropeuk.eu/other-eu-funding-case-studies...
It does seem Denmark doesn't need to do this at present.
When they say other countries do more funding, they are not wrong. But we don't talk about Czech film/television production in the same way we talk about the Danish counterpart.
There are plenty of film makers out there who still think television is beneath them, and I am sure some of those film makers are Danish, and they therefore cannot cash in on the Danish television success.
I find that very hard to believe. After all, Lars von Trier (the most famous Danish director) made a tv series ("The Kingdom") and all the biggest actors (like Mads Mikkelsen) have had roles in tv shows. The less famous people in the business are typically just happy to be employed.
https://en.wikipedia.org/wiki/Movie_production_incentives_in...
"The Rain" is unique in being financed by Netflix.