The two are related. In practice no indictment will issue if the prosecutor doesn't think they can win without the defendant's testimony, and in practice the defendant's statements to police are used to impeach them at trial (because the hearsay rule allows that hearsay) and thus make a part of the case just as much as if they made those statements in court, in the witness box. No case -> no trial, no trial -> definitely no testimony.
Watch that video. Then watch it again. Schedule a yearly watching or three.
