Casey's thinking is so sociopathic, she may have thought of using her daughter's death for her own gain by staging a fake kidnapping, therefore garnering her mother's sympathy and that of everyone else. Casey may have even thought she would become famous as the sympathetic mother of a kidnapped child and then all her problems would be solved. In this scenario, after Casey found Caylee dead, or killed her accidentally, as the case may be, Casey chose to apply tape to Caylee's face to make it look like a stranger abduction - the police were supposed to think that a stranger taped Caylee's mouth - for surely her grieving mother wouldn't do that. But for some reason, Casey didn't carry through with the plan and never went to police with her story and after 31 days, it really was too late to do that. So when Cindy cornered her, Casey was unprepared and spouted some garbage from the never fully concocted kidnap story she had imagined, but had not thoroughly reasoned out.
