If you read any of the "mommy" boards they are flooded with horror stories, daycare issues, enough to stop any parent from putting their child into daycare of any kind.....but at the same time parents need to get past all the rhetoric on those boards and be a bit more realisitic. I know trust is part of it and common sense goes with that - one of the reasons a person just starting out has so much trouble getting that first client compared to the caregiver with an almost full house in that if others are there it must be ok.
Beyond this parent's insecurities is the way she went about gathering her information - bet she checked the caregiver out on facebook, etc. too. Reads too much, is reliant (gullable) to what others tell her - which can be a good thing if she starts taking advice from the caregiver instead.
While "next" is certainly the best choice if you want to pursue this potential client or want to help her not make the same mistakes next time then you could call her if you have her number or email if you don't. Let her know that your current clients made you aware of the questionaire and that you advised them that they were under no obligation to fill it out. That you thanked them for their time in speaking to the parent on the phone but that that was where their obligation ended. It is then between the potential parent and the caregiver to work out further details. What is coming across is that she is trying to call you a liar in a sense by asking for confirmation that what you said in the interview is true.
Depending on how old the child is, have they been in care or in care now in what is not a good relationship and the parent is afraid of getting burned again. In that case I would have a bit more sympathy, bring it to her attention and ask how you can help her work through her insecurities - if she takes offence to being told that well she wasn't going to work out anyways.