This is correct. Ugg tried to patent it as a "brand" name all over the world and then tried to sue all company's in Oz who dared to call them Uggs. The Ozzies proved that Ugg (or Ugh or however you spell it) is an australian generic term for sheep skin boots, and thus Ugg are no longer allowed to sue any company in Oz.
A Onesie, on the other hand, is Mother Nature's intervention in the human population of the earth. She's had enough, there are clearly too many humans overpopulating the planet, so she has invented the Onesie.
Buy one... and your sex life is OVER!