I don't think there is any way to adjust it or even change the DNIe mode like Samsung allows. People wrote custom kernels for the Nexus 4 to allow color adjustment but there aren't nearly as many devs working on the Moto X, so you're probably stuck with what you get. I don't imagine that they do any factory calibration to speak of, so of course it will vary greatly between panels.
Unfortunately, oversaturated is the new properly calibrated. The problem is that it has a better off-the-shelf look when people who are clueless are comparing models in the store--hold a Moto X or GS4 up next to an iPhone or Nexus 5 and the colors "pop" more, which seems to be more appealing to the average consumer than the more muted appearance of a display with proper sRGB calibration.