Hard to dispel unfounded obviously false notions like this. I could on and on as to why their suggestion can't be true, but it'll be like arguing religion, they just believe. Ditch them as a client, if this issue has to be fought, there will be a never ending supply of more like it.
Anyone who claims to track fraud, has a vested interest in reporting fraud. There is some fraud, always, look hard enough and you'll find it. Banks do get robbed, but crazy me, I still keep my money there.
Sorry, I know this post wasn't helpful.