Low quality fluorescents run in the range of 2,000-3,000K.
The color temperature as shown in degrees K (kelvin) relates to the color of the output light. The scale ranges from infrared to ultraviolet and perhaps beyond. The light of a match is around 1600K (deep yellow), an incandescent light bulb - 2800K (yellowish-white), moonlight - 3500K, daylight - 5500K, and a xenon arc lamp - 6420K (blue-ish white). The higher the number, the bluer the light. Conversely, the lower the number the yellower the light, finally gaining a red color as the color temperature gets very low.
I follow you up to the 6420K xenon arc lamp --
but my question is, what does a 9600K bulb look like? Does it mean it's a blue LED? The description says super white LED -- but I haven't seen anything beyond the 6000K to have any idea what that might look like -- if it is at all possible.
All the others are in the 5-6000K range -- that they're selling on that site for LEDs -- with that one very notable exception. It seems like that one's out of the ball park.
That's what piques my curiosity.
Color temperature is a means of specifying whether light is reddish, bluish, or neutral, but it doesn't really imply anything about spectral quality. One could achieve a seemingly "white" light by combining in proper balance the output of suitably-chosen blue and yellow LEDs, but even though the light itself looked reasonably white, the colors of any objects illuminated by it would be way off. Some green objects may look yellow, others blue, others dark, and others light, but none would look green. Even if all the green objects looked similar under daylight, their appearance under a bi-spectral "pseudo-white" light could be totally different (note: this could be useful for adding anti-counterfeiting features to currency).
One thing I'd like to see in a review of fluorescent lamps would be a comparison of their spectral plots. A computer display isn't going to produce a spectrum that matches a fluorescent lamp, but a spectral plot could show the spectrum anyway.