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Is that really correct though?
If she is guilty of FDM and she does that she is looking at the DP or LWOP depending upon how she reveals it the the State. I doubt this would be an acceptable outcome for ICA.
Frankly, if I was in her position I would feel the same. I appreciate those that say if they murdered their child (something - I might add - that she has not yet been found guilty of) that they would count themselves lucky with LWOP. I doubt I would though and am unsure that it is something you could properly predict without actually being in that situation. Also, "sociopaths" and/or people who do murder their kids for reasons other than due to temporary mental weakness after birth (post-partum depression, etc) may have a totally different outlook than "normal" people.
On the other hand, if she is guilty of killing Caylee by way of neglect or if it was an accident the consensus here is that the prosecution won't accept a plea on that basis. So it seems unlikely that "telling the truth" would be much assistance to her in this scenario.
In short, whatever is the "truth" I am unsure if it is in ICA's interests to tell it prior to a plea deal. As I understand it rarely does one any good to speak to the police/state at all in the USA.
Now, if the state have offered something like 2nd Degree Murder with a stipulation of no life or aggravated manslaughter or something that would give her a reasonable and realistic prospect of release I could certainly see why she should accept such a plea.