I haven't read the NYT article, but CNBC has a really good piece on this that lists Snowden-leaked NSA/GCHQ documents revealing:
1. How they use their position to water down/penetrate encryption standards as they are made
2. How they occasionally work with hardware manufacturers to ship back door-laden gear being sold to "targets of interest" (You've got a Dell! It's the same one that Kim Jong-Un ordered!!)
3. How the GCHQ is working towards penetrating 300 VPN streams
4. How the NSA's program to help IT product/service providers validate the security of their offerings is also used to engineer NSA-friendly vulnerabilities into those offerings
5. How the NSA got slapped down in their effort to openly insert a trap door into IT gear with their 90s "Clipper chip" program, and has since been working on a multi-pronged approach to do the same thing surreptitiously.
It's a good read: