Travel from the United States to Faroe Islands

The Faroe Islands opened travel for holiday in April 2021. As long as one is vaccinated, there is no quarantine requirement, but still have to be tested for Covid prior to leaving and when you land. However, the travel rules for Denmark seem to be in contradiction to that of the Faroe Islands. If I were to travel through (transit) Copenhagen, the Danish government says I can travel on holiday through the airport, but not to the Faroe Islands. This doesn't make sense to me since the Faroese police have already informed me that I could go on holiday there, but the Danish government won't let me transit through the Copenhagen airport, even though you can transit through on holiday as long as it is not the Faroe Islands or Greenland. Has anyone experienced traveling through Denmark to get to the Faroe Islands and was there a problem? Thanks.