Maybe she was talking about gdiapers
http://www.gdiapers.com/. They are a disposable/cloth hybrid. I wouldn't be able to use those either. My toilets wouldn't stand up to flushing the pad.
I do provide service for cloth diapers, but I have certain specifications as to how and what I will use/do. Totally your decision to not provide the service though.
I can't believe they didn't get the point. I guess when they call back say that you thought it over and really do not think you are a good fit for their family.
I don't know where they think they are going to find a daycare where their kiddo is never going to cry, funny.