This isn't so much a business-client story, but it does involve some otherworldly stupidity by a member of the general public.
I'm a graduate student in Geology; specifically, I'm a mineralogist. Occasionally members of the general public come into our building at the University and ask us about unusual rocks that they've found. I enjoy teaching people, and the professors usually can't be bothered to deal with them, so they're often redirected to me.
One time a man came in with a chunk of sandstone he claimed to have found out in the desert somewhere. He thought that one small grain might be a diamond, and he asked me to verify this. He pointed to a small black spot on the rock. It wasn't shiny, and it was opaque, so I'm not sure why he thought it was a diamond. It was hard to crush his hopes, but my explanation was inevitable:
"See how the black just rubs off on my finger? I'm afraid that's a scrape of black paint."