I'd bet quite a bit, though not "my life", that they do not have a generalized "read everything" ability for all forms of SSL. They may have what cryptographers would call "a crack", but that's a low bar, and doesn't prove they have a practical attack.
However, DDG is currently using 128-bit RC4, which is very weak. [1] I wouldn't care to bet anything that the NSA doesn't have an RC4 cipher crack that is practical to run on wide swathes of traffic.
RC4 is very popular, which I believe is because some people claimed it was a defense against the BEAST attack. I researched this for work, and I couldn't find anyone whom I trusted saying that was a good mitigation. The people I trusted merely observed that RC4 was not vulnerable, but never said you should switch to it. Only secondary sources ever suggested that. My conclusion was that there was a reason for the primary sources never suggesting that; in response to a theoretical break of the rest of SSL, the correct move was not to move to a solution that had much more practical attacks already known than what BEAST demonstrated. But now it's even sillier; BEAST has been either entirely or almost entirely mitigated in browsers (there's no server-side defense against BEAST, but there's a client-side one you can use, and browsers now have it). As far as I can tell, RC4 should be abandoned and we should resume using stronger ciphers for SSL. Anyone still concerned about BEAST should update their browser.
[1]: http://nakedsecurity.sophos.com/2013/03/16/has-https-finally...