Then, after a little more digging around, I found a nice article by Bill Nye (the science guy), who describes how this oleophobic iPhone feature works. Here's a brief excerpt from his article:
"The Applers were able to do this by bonding this oleophobic polymer to glass. The polymer is an organic (from organisms) compound, carbon-based. The glass is nominally inorganic, silicon-based… solid rock. The trick is getting the one to stick to the other."