Several posters have stated that they believe there is some small basis of truth in Casey's stories. I think so, also. So I tried to put together some of her statements with some of the observed facts to come up with any possible scenario where she could NOT know where Caylie is, yet truly still have convinced herself that the child is "at the beach with the babysitter". Since Casey is well-tanned and also often seen in pictures at various clubs, perhaps she took Caylie to the beach for a way to entertain her and still have a relaxing day for herself after a late night out.
Often older children at the beach will offer to play with and "watch" younger children whom they have just met that day there on the beach. It is possible that Casey let them play with her and then fell asleep. IF so, anyone who was watching this scene could have told the children that Caylie's mom wanted them to take her for a walk, or to go get some lunch, etc. If Casey woke up to find her gone and the other children no where around anymore, she would panic, feel guilty, irresponsible, ashamed and a million other things. Maybe she did have some sort of a mental breakdown and convinced herself that her child is still with those children and their family being "taken care of" at their beach vacation.
I realize that this is something that is pure speculation, but it is at least one scenario that might explain how she lost her daughter....even though it can never explain why she would not immediately ask for help to find her.