I'm definitely not calling CPS and getting her taken away from her parents, they're not neglectful they're just oblivious and I realize it sounds a lot worse than it actually is.

Well... hopefully. You're not privy to their home life, so you don't really know what goes on there. That sort of behavior from a child isn't normal - either there is something going on in her home life, or she's severely emotionally disturbed. Either way, the problem is obviously not being dealt with properly - if it's the former, CPS needs to be involved, and if it's the latter, I don't understand why her parents aren't taking her to a child psychologist/psychiatrist/therapist who can figure out the root of the problem and implement a treatment plan.

I think the first step might be to sit down with her parents and just explain to them that I'm concerned about all the lying and that if she does it again I'm quitting and calling CPS.

I'm not a lawyer, but just remember... it's going to come down to your word against hers unless you have some sort of video evidence to back yourself up. If the confrontation turns sour, you really don't want to find yourself in the sticky situation of having zero evidence to corroborate your side of things. Even though you're not doing anything wrong, you don't want to find yourself in legal hot water without a way to prove, without a shadow of a doubt, that you are completely innocent and that the kid's just making shit up - I'm sure with a bit of googling you'd be able to find more than a handful of cases where a child bullshitting like that has gotten adults in a lot of trouble.

I'd suggest a nanny cam.