Cheap garment-factory labor doesn't always equal cheap clothes.

The availability of low-cost workers has sent mass-market clothing labels of all stripes— H&M , Gap , Wal-Mart , Zara and others—into Bangladesh's $20 billion garment industry.

But designer brands including Giorgio Armani, Ralph Lauren and Hugo Boss also have outsourced manufacturing to Bangladesh, where worker safety has become a huge issue following several fatal accidents. Indeed, high-end labels often use the same factories as their discount peers.

Giorgio Armani last year received shipment of 21,600 pounds of T-shirts and underwear made in a factory in the port city of Chittagong, according to the shipping records. A nearby factory supplied women's pants to Michael Kors.

Armani said the Italian fashion house produces a "relatively small number of items" in Bangladesh. "The commonly held assumption that all manufacturing conditions there are inadequate is not a fair reflection of the reality of the situation and does that country a disservice," Armani said.