For the same reason that an average hacker would have a much better knowledge of the code for various daemons than the sysadmins who administer them - they're reading critically and looking for vulnerabilities where the actual semantics differ from the purported ones. I've no doubt that what the NSA does actually is "constitutional" under the common corrupted interpretations of it - government programs are structured to avoid mortal conflicts with the constitution, sympathetic or even just probabilistic courts then assert that specific facets aren't actually over the line, and severable agents acting "independently" informally make up the difference.

Law is akin to code, and suffers from the same complexity-induced limitations that end up as the halting problem. With enough indirection, meanings and definitions divert wildly from what they purport. This divergence starts as soon as abstraction enters the picture - for example the widespread tendency to see rights as "primitives" that are acceded when forming higher-level emergent structures. Participation in the higher-level structure becomes de facto mandatory, and those purported rights end up nowhere to be seen. And once this erosion process starts, it becomes harder and harder for anybody to see that their rights should apply universally, rather than just in a nondescript wood shack on unincorporated land in Wyoming.