I saw an interesting example of mosaicism in a medical journal. An infant was born with half male genitals, half female genitals. The most obvious explanation was that he/she was born of two embryos, one male, the other female, that combined at an early stage (but not too early) and formed a mosaic individual, with patches of male and female cells. Mosaicism actually is pretty common in biology. Sometimes you get patches of skin that vary between 2 colors. The later the embryo recombines, the bigger the patches are.
That has nothing to do with recombining of the embryo (don't know about the story You mention, there it can be an explanation, I am talking about the 2 color story, e.g. a cow or a dog, and mosaicism in general), the different patches exist because of mutations in one embryo. These mutated cells will divide just as the not mutated ones. And the sooner these mutations occur, the bigger the patches will be. And You don't need a stem cell or organ transplant to get mosaicism, You get it in the woomb.