Are you looking for more oversight than is expressed in the article? It says the Danes check to make sure what the NSA searches for on that system does not include Danish citizen identifiers.
At the end of the day, this will rely on trusting the NSA despite their dubious history.
Even more surprising that DK hasn't been paying attention to any of that apparently...
Governments that gate human rights on nationality are fundamentally amoral, and should never be trusted to self-regulate.