Not only would the killer probably not say anything to give himself away, but Columbo's whole strategy depended on that admission. Columbo is always a brilliant detective who repeatedly makes his suspects more and more uncomfortable until they realize that the rumpled, sloppy, forgetful dummy act was JUST an act. By that time they've played his game and fallen right into his trap.
But in Last Salute, he catches his prey with "T'isn't". A horrible letdown in a bizarre episode that completely breaks Columbo formula, i.e., we don't know who the killer is until the end, Columbo has not one, but two partners, plus there are numerous "jokes" (I hope they were jokes) that didn't fit.
I don't know how this episode got made. But I must admit that I am fascinated by how truly strange it is.