All other things being equal, why would it matter if a suspect instead of saying something obviously incriminating, had instead said something diametrically opposed? Is that what you are asking?

If so, I'm confused. Why wouldn't it matter? Wouldn't this necessarily only be the case where the Google search doesn't really matter at all (i.e. there is sufficient other incriminating evidence).

Anyway I also think you're missing what was merely meant to be a comment in jest. But now I'm actually confused what point you are trying to make.