It seems to me that the police would have been happy with a confession from Kate that they'd disposed of the body, never mind if they'd committed some grisly murder first. That constitutes a deal does it not? Case closed, a conviction, never mind what really happened...
You still do not appear to understand the full importance of the PJ, via Carlos, explaining that if Kate admitted to body disposal, the maximum sentence would be two years. Try thinking it through from the view point of the PJ. Why would they try to get Carlos to explain this to his client?
Kate viewed 2 years for a crime attracting a maximum of 2 years as a deal. You and other supporters seem to classify it as a deal. I know for certain that stating the maximum was 2 years constituted no deal. And since this went via Kate's lawyer, a man who would fully understand that the PJ had no power to set the actual sentence lower than the maximum, any notion that Kate was 'offered' less than 2 years is contrary to common sense and that which Kate herself wrote.
Why would the PJ get Carlos to explain the maximum for body disposal was 2 years? Think, Alfie, think.