C + C Music Factory band name meaning

Band, or rather: producer duo from New York, specializing in dance and club music, but not averse to making musical excursions into pure pop either.

Originally staffed by Robert Clivillés and David Cole, but reduced to solo act by the death of Cole in 1995. The first letters of surnames Clivillés and Cole seem an obvious explanation of the origins of the band name, but the story goes that the source is to be looked for elsewhere.

At the C & C Clothing Factory to be exact, a garment factory that supposedly was given the nickname C & C Music Factory because of the noise the machines made. 

Problem: a reference to such a factory is nowhere to be found. That does not change the fact that it is a pretty good story.