This is a reasonable theory. But just suppose this were true. Wouldn't Casey have asked her parents for the money by now? Surely they could've used the money (second mortgage) that they used to get Casey out on bail.
Further on the "Just Suppose" -- yes, I'd agree with you that it would seem Casey would have asked her parents for the money to pay the babysitter.
However, I can think of one reason why that might not be something that would work. If there may have been a babysitter, it could have been a woman who was in this country illegally. She may have never told Casey that. In fact, she may never have told Casey her actual real name. The woman could have completely lied to Casey about every single thing she said. The woman could have said her name was "Z F-G". She could have said she lived in such and such apartment at Sawgrass. She could have arranged to meet Casey at times there at Sawgrass (at the bottom of the steps or somewhere on the grounds) so as to give the impression she lived there. Maybe most of the time she met Casey other places such as this or that park or whatever.
And maybe this woman who was here illegally decided to leave the country and simply took Caylee with her, without regard for Casey whatsoever. If someone did something like this, she's not going to surface because she did in fact kidnap Caylee and she would be investigated if she turned up in response to the reward offer. And Casey is left stuck with a name that does not connect to the person she knew, addresses and locations that don't connect, etc.
Please Everyone -- this is entirely HYPOTHETICAL. I am not going to discuss the reputed evidence that Caylee is dead at the hands of her mother. I'm simply offering a possible "how" with regard to the thread question and my thoughts on just that.