Dave, it's my understanding (from reading these boards in the past) that what happened is... someone messed around with an otherwise very good script. Someone (???) took things out of the script and added other things, and perhaps moved some other things around. In the process, they got so close to the script, they couldn't see that it nolonger made any sense. Or at least, that the ending didn't make any sense.
So no, Columbo doesn't actually prove anything. The murderer gives up only because the heavily-edited script tells him to.
Who was it that SOME people think messed up the script? I could give you --->6<--- clues. But I won't. Be seeing you!