I think I can expand a bit more on this as well. 4300K referring to color comes from the concept of blackbody radiation. Don't worry about the term, for our intents and purposes, it just means something that gets hot and radiates light when it is hot. The thing about this type of radiation is that it has a continuous spectrum, that slowly rises and peaks at a particular frequency then decreases. This peak is directly related to temperature, the higher the temperature the higher the frequency at which the peak occurs. This is why stuff gets red hot, then white hot then blue and so on as it gets higher in temperature. The thing to reiterate is that this spectrum is CONTINUOUS, from IR to UV. HIDs are NOT this way. HIDs are a line emission spectrum, meaning that the emission spectrum is not continuous, it is just a series of lines (I can get into why but no one would really care). Due to it NOT being continuous, it CAN'T have a true color temperature. You can get an approximate, though even then, some colors will not be present and others will be overly present. This is why HIDs "color temp" is so variant. Depending on the approximation it can vary widely.
Another note about the line spectrum. This line spectrum is why HIDs are so efficient compared to halogen bulbs. Due to the spectrum being continuous tungsten bulbs physically HAVE to emit a certain percentage of their light in the IR region. The line spectrum of HIDs allows that percentage to be much lower. More energy can go into the visible region, less is lost as heat. Along with that, this is also why HIDs have a much lower CRI. They don't have the full spectrum so some colors don't appear quite right.
