UL is private company that sets safety standards and tests products that
  manufacturers voluntarily submit for (and pay for) testing.

Why do these manufacturers do that? Perhaps just as a lawsuit hedge: they can always claim to have been 'certified by the de facto testing standard', in which case it's the reasonable expectations laid down by the law that drive the interest in this 'independent' testing. I.e.: the government.

Another explanation is that large brand A initially wanted to distinguish itself as 'the safest' and brand B just followed the lead so it didn't seem less safe. When they control a substantial part of the market, others will soon follow. After that, the actual contents behind the logo don't matter anymore. It's a perception-driven protection racket, the actual value of which cannot be determined by consumers. But it doesn't even matter how it comes about: after most of a market sports a certain logo or association, what's to stop that organisation from growing lax and pleasing their clients? There is hardly any room for competition in that market: who's going to start a UL competitor and why on earth would a brand be interested?

Or, the more fundamental question: who tests the testers? How do you know the UL is not theoretical and actually working? Even the government suffers from corruption; I doubt such companies are any better.