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 citizen

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).