The fact is that there was a scientific report by two people named Deborah MacFarlane and Carol Alonso which *overestimated* the exposure of client skin to UV light emitted from UV nail lamps and improperly characterized the effect of these lamps on the hand. The studies looked at two - yes TWO - women who both lived in Texas and contracted skin cancer on their hands.
Unfortunately the media has run with this and it is now one of the most believed nail myths out there right now.
Linked here is an article with the details on how the report was wrong. It truly is a fascinating read.