My opinion -- and it's worth every penny you paid for it -- is that if all of the components are UL listed, and they are installed according to the manufacturer's instructions, the cordset should be safe.
As for the set quoted as "non UL" they may indeed be made of all UL listed components, installed according to manufacturer's instructions, but the fully assembled cordset is not itself UL listed. Perhaps the manufacturer does not have authority to market cordsets they assemble as UL listed.
UL listing applies to the full assembly of a product, or to particular subassemblies. For example, a replacement plug with the UL mark simply indicates that subassembly has been tested and listed by Underwriters' Laboratories. In order for the cordset to be listed, the manufacturer would have to provide a sample cordset of the same design to UL for inspection, testing, and listing. Alternatively, UL provides means for manufacturers to become listing agents, so they can "list" some of their products without submitting them to UL.
Your insurance company may have something to say about this, as well.
