Presented by Spiegel are internal services that are designed on purpose to be more economical. They exploit more bad implementations. It doesn't really matter as long as the dirty tricks get the work done.
Also, NSA seems to troll for targets from the vicinity of their targets of interest. It is again more economical, and can be just as revealing. The risk there is that the broken target has nothing of use. The real movie style "let's break the encryption keys" stuff is done for sure targets when they get the extremely rare high value target on platter.
There is no known algorithm that can break a properly generated RSA key of that size - the work required with GNFS is equivalent to brute forcing a symmetric key of something like 280 bits. Anything that could do that should be able to break even 4096 bit RSA keys (~144 bit security) pretty much instantaneously, and their problems with PGP pretty heavily imply they cannot do that.