A statement is not a scientific fact. The head of the NSA lied to the American public about their extra-legal monitoring. What has changed since the Snowden revelations? Why would Danes be more respected by the NSA than US citizens themselves? This makes absolutely no logical sense.
To your point, the IC trades in misinformation and distraction as much as it trades in truth and fact. When any of those acronyms make a statement it's fitting to wonder if there's a broader arc, a bigger picture.
Their responsibilities and mission are clear. There are no style points. They'll do whatever it takes to accomplish that mission. History is very clear about this M.O.
An interesting thing is no one is willing to say "lies" anymore. It's always "misinformation" because it gives the perpetrator a way out to claim it wasn't intentional. The NSA and CIA do LIE.
This has nothing to do with scientific fact? It's about risk/reward for NSA. If Denmark finds out that they were deliberately using the system on Danish citizens, the NSA risks losing access to the system. Not taking that risk in exchange for having to use other methods to investigate Danes sounds like a perfectly reasonable risk/reward calculation from the NSA's point of view, especially considering how small Denmark is.
I mean, sure, they can lie about it, but that always carries a risk of being found out. Especially considering it sounds like from the article that FE can see who the NSA is searching for (and even has to approve the search queries).