You appear to be missing the point of parallel construction. The point is that they show a true, but-not-the-whole-truth "hand" (the parallel construction) while obscuring the full truth. That is, you spy on someone, and obtain a bunch of evidence, either illegally or that is fruit of the poisonous tree. From that knowledge, you construct a (fictitious or only partially fictitious, but plausible) story about how you gathered enough evidence to incriminate your victim, without revealing that you came across this evidence illegally. See http://en.wikipedia.org/wiki/Parallel_construction.
Yes, they are legally obligated to not lie about the true means of how they came to have the evidence. But if nobody can prove you're lying, they can't call you on it.
