How can an atheist or Jew Baptize? It's my understanding that a Jew or even an atheist can perform a baptism if they use the proper form and matter, with the correct disposition, which is, to do what the Church intends. How can an atheist have the right intention if they do not even believe that Original Sin exists?
The idea you are paraphrasing is ex opere operato, the idea that the sacrament is in itself efficacious and does not depend on the intention of either the minister or the recipient. Not all denominations hold to it. Those that do, probably have nuances in their application of it. The historical origins of this viewpoint go back to the Donatist Controversy in the 4th century. Back then the schism was between ex opere operanti and ex opere operato.

Here are a couple of links explaining them both in more detail:

Ex Opere Operato (New Catholic Encyclopedia)

Ex Opere Operanti (New Catholic Encyclopedia)