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.
The data used by XKEYSCORE is stored on multiple servers, including the NSA's long term storage servers. How could the Danes be certain the NSA wasn't conducting searches from some cache they do not have access to?
At the end of the day, this will rely on trusting the NSA despite their dubious history.
Part of the Snowden revelations was that the German BND was also granting this access. The NSA sent so many keywords that the BND basically stopped checking, and looking at it in an investigative committee of the german parliament they found a massive amount of clear domestic espiomlnage (keywords like 'Siemens' or product/technology names). Basically the BND was too incompetent to realise they were enabling US espionage on their own companies. Insane but true. You could and should blame the BND but honestly what kind of partner is the NSA if you can't even trust them on such basic level?
Even more surprising that DK hasn't been paying attention to any of that apparently...
The very concept that people should have their basic human right to privacy protected or denied based on the happenstance of their location of birth is insanity.
Governments that gate human rights on nationality are fundamentally amoral, and should never be trusted to self-regulate.