We know that our DSLR (seen as a black box) are not that great at dealing with subtle differences in illumination near their saturation point. I believe that this impacts their ability to distinguish subtle colors as well.
That's only true with some cameras, at the lowest ISO. The sensor can be non-linear near saturation, or the the camera may stretch the highlights to make it appear that the full range of RAW values are used (such as the Canon 20D, which should really have had a base ISO of about 115). Even then, there is a potential for a RAW converter to have specific information about a camera, by running a series of tests, to see how linear it is, where clipping occurs, detect fixed pattern noises, etc, to give optimal conversions from that camera. I've never heard of any converter offering this possibility, though.
Is Fuji only playing with the values after capture, of does their sensor really capture color with more quality (resolution) that say Canon or Nikon? Nobody knows for sure, but my (mostly unbustantiated) belief is that their sensor might be able to capture both more colors (wider gammut), but also to differentiate more subtle color differences. This is another area where there might be a link with bit depth since it would take enough bit depth to differentiate the hues captured by the sensor.
More bit depth would help, but it only helps when noise is at bay. Noise is far more significant than bit depth in most current cameras. Quantization of RAW data is not an issue with current cameras. You see quantization in the output for two reasons:
1) An optical illusion, where your mind groups similar colors of individual pixel noises as similar - imagine a canvas of grey 128, and a dozen isolated squares of blue, all with slightly different values - do they look any different to you? You may have to use the info tool, or exaggerate the differences with the levels tool to tell them apart.
2) Converters don't use enough bit depth - no room for extended precision in the deepest shadow areas, and noise-softening applied too agressively in the highlight areas. A tiny amount of noise is always good, when your display medium is posterized.