"Distinguish" means "tell two things apart", e.g. one household from another. It doesn't mean "identify".
Fingerprinting is likewise a means of distinguishing, but not necessarily identifying. The need for law enforcement to identify is where the need for the logs arises.
I assure you that I don't care about whether I'm right, I just care about the reasoning and what the correct conclusion is. If being willing to engage in discussion about something comes across to you as wanting to be right, that's just your personal inference.