I love how the politicians presume NSA is safe partner and their danish citizens are not in the data. It does not really help if every other neighbouring country does the same. NSA will get danish info elsewhere. Everyone gets played. It works as long as USA is an trusthworthy ally. They wouldn't dare to abuse the information for private gains... right?
In a larger sense, the arrangement might, to a degree, defeat the purpose of having separate foreign and domestic intelligence agencies, but that is a more abstract notion. I guess we'll see what the Danish public will think or do about.