The problem with that rationale is that using it they have a "information-gathering" crew could go into your house collect everything, have the investigation-crew talk to people and then have "suspicion of reasonable cause" wherewith to get a warrant and go through your things.
No good will come of this.
So, the practice of over-sampling (if you will) has no downside risk. None. The bootstrapping issue you raise doesn't exist for the investigators. They have to have suspicion before they can access your NSA file, and armed with suspicion, they can easily get a warrant.