This senario is not likely. I do not believe that Westerfield had any intention to confess. There is no credible information about this fact. The only thing you have here is a rumored plea bargain offer that is absolutely a normal practice and is usually offered by the procecution.
IE: "Look here MR. Atty., we have all this evidence, we know your client is guilty so why don't you tell us where the body is so that we can bring closure to the family. We will not go for the death penalty in return."
My contention is that this is all that happened here and Brilliant Bill O'reilly has stuck his foot in his mouth again!