Check out [1]. Seems to be a combination of pre-flight calibration tests and in-flight observation of stars and planets with known optical characteristics.
Interestingly enough, I think that's exactly how the Curiosity rover calibrates its camera, though it's the camera on the robotic arm looking at a fixed test pattern.
I think they usually have a black and white camera with filters of specific wavelengths, some of which roughly correspond to red, green, blue, and they combine them. The color pictures I've seen from Mars and Cassini usually say "approximate true color."
They have no green (495-570nm) filter, just panchromatic (400-975nm), blue (400-550nm), red (540-700nm), near-IR (780-975nm) and narrow-band methane (860-910nm).
Does it really matter? I remember reading about this in one of Richard Dawkins' book (I think its Unweaving the rainbow). Now you can complain about the Crab Nebula, whether its color correction, or you are lucky enough to view it up close with a naked eye.
The colors you observe are just models of the different frequencies which our brain has evolved into to label as "red", "violet", or "#782". :)
A much less/more evolved brain (be it alien or terrestrial) will observer it much differently.
I'm guessing there isn't a robotic arm holding up a test card in front of the camera :-)