It's probably why that's what's getting the play. Not a lot of clickbait in a discussion of Denmark's share of the NATO budget, or Danish politicians afraid of a Trump visit ginning up their nationalist opposition.

Also, nasty is not really an extreme criticism or superlative adjective. It's not like saying mean or evil, the connotation pre-SJW was minor unpleasantness. Presidents during the Cold War would not have called the USSR or China "nasty", it's just a minor criticism. The idea that it means gross or disgusting is relatively recent. It was "not nice" after "naughty" began to have a sexual connotation.

I personally thought he was good humored about the reaction, such as retweeting a macro image of a gold building with the word "Trump" on top, photoshopped onto the Greenland coast, with the comment "I promise not to do this to Greenland."

And, thinking about it, if there is an issue of contention regarding Denmark's share of the defense bill of our alliance, it kind of IS a concern that the overwhelming majority of Danish territory is RIGHT OFF our coast (okay, Canada's, but it's not like they count), and they don't bother paying much money to defend it. I'm pretty sure we have defense installations there, and it would be a lot simpler to own it outright, rather than have to deal with the politics of another country's autonomous territory right inside your defensive area.