Earlier quoted context omitted.
That might be the definition of "investigative police work", yes. That's not what I've observed in practice. And those that know better than I advise against giving up evidence with the idea that it will "help your case"; re: the "don't talk to the police" video that is so often referenced here.
So you think that, for instance, if the police are investigating you in connection with a bank robbery while you were in another country speaking at a conference, you should not tell them that? What about if you are wanted for questioning about a murder which involved dragging the body a significant distance while you were in the hospital recovering from chemotherapy? Still don't talk to the cops?
Nope. While you're busy playing "what if...", I'm dialing a lawyer. Should that trained professional advise talking to the adversarial trained professionals, then I would do so, and not before.
I don't how it is where you're at, but in the U. S. cops have demonstrated time and again (and I've seen with my own eyes) that they are not concerned about truth and justice, but arrest and conviction rates. I'm not walking into that scenario running my mouth without professional advice.