Leadership can be conducted many different ways, from highly hierarchical to very egalitarian.
From Harvard Business Review:
"This scale gauges the degree of respect and deference shown to authority figures, on a spectrum between the egalitarian and the hierarchical. The former camp includes Scandinavia and Israel, whereas China, Russia, Nigeria, and Japan are more hierarchical."
While USA is not mentioned above, notice that where Denmark is way out left on the 4th component, USA is in the middle - and that is much more hierarchical than Denmark.
Deference is not a concept much applied in Danish culture, and if somebody expects deference, or even worse, behaves as if he or she is entitled to such status, such a person will likely be very disappointed with his or her Danish underlings.
This should not be mistaken for lack of respect. Danes just want you to have earned that respect. Not only with your Board or CEO but in your individual relationships with them.
For Danes working in USA, this can lead to problems exactly because more hierarchical oriented managers may feel disrespected. As Americans tell each other that they are very egalitarian - "just call me Bill" - they don't realize that what they feel is may stem from their Danish employees treating them as colleagues, not as "their betters".
As managers of Americans, Danes may be surprised if their employees don't self initiate but expect more pre-approval than their fellow country men and women. Some of this is also related to the communication style where Danish managers may suggest something but such hints will not necessarily be picked as instructions to do something.
Generally, when Americans have gotten used to having a Danish manager, they appreciate the higher level of autonomy that a more egalitarian structure gives them.
There is with movement towards lean development a dawning realization in USA and Silicon Valley that the American business culture is not as egalitarian as previously thought and that this can hamper the agility of the organizations.
Management style is one area where the caveats mentioned in the first post in this series should be taken into account. The American organizations who have participated in this research may be much bigger than the Danish companies. Consequently, more hierarchy could be expected just from size.
Although many start ups in Silicon Valley are relatively small for USA, many have employees from countries with more hierarchical attitudes than USA. Even in Silicon Valley, Danes may face the issue of different expectations, both as managers and as employees.
With the perspective of an American working in Denmark, a great article here.
(For Danish readers, more on the subject here.)