There is no right or wrong here Frans, there is only how close you think you need to be and how close you think is useful. Both are fair questions and both have been studied for a LONG time when it comes to correlated color temperature. If you're really interested in it, there is a tremendous amount of literature going all the way back to the 1920s.
Originally the idea of CCT was to find the temperature of the Planckian radiator with a perceived color most closely resembling that of a given stimulus. This has been problematic to define experimentally. The CIE came right out and said it:
"The concept of correlated colour temperature used to be based on visual observations. Recent investigations have shown (see Borbely et aI., 2001) that no metrological definition can be based on such perceptual investigations."
So what do you do? The current practice is to use a colorimetric definition based on euclidean distance from the Planckian locus on the uv chromaticity diagram. There are a couple ways to go about this. The easiest is to use C. S. McCamy's simple polynomial approximation which will allow you to calculate the CCT from xy coordinates with a great deal of accuracy. But this accuracy is misleading because it is related to the math, not observation. The formula doesn't care whether you calculate to the nearest 100ºK or to the nearest millionth of a degree.
Another way to do this is based on a binary search through the locus comparing the distance to the stimulus you're testing. You basically start with a temperature, find the the uv coordinates on the Planckian locus and find the distance to your stimulus. Then move to the next value and test again—if the distance shrank you continue, if it grew you move the other way and eventually you narrow in on a value to whatever precision you like. It's computationally easy, but slower than the formula. The method requires that you answer the question how much precision do you want?
If you do this with your xy coordinates and decide you only need precision to 100ºK you find the answer is 4700ºk—which is what Solux published. For a lightbulb manufacturer, this is entirely appropriate since you almost never see bulbs specified with any more precision.
And from a colorimetric standpoint it actually might be more
precise the appropriate. Borbély (the same on the CIE cited above), Sámson & Schanda in Wiley's COLOR research and application
in 2001 write this about CCT:
The experimental determination of correlated colour temperature is too uncertain visually to be correctly definable. Thus, we would like to recommend using this term only as a first estimate of the chromaticity of near-white illuminants. For describing lamps and displays, a seven-value scale seems to be adequateThe Concept of Correlated Colour Temperature Revisited
Their seven-value recommendation rounds CCTs to 2700, 3000, 3500, 4200, 5000, 6500, 9500. While you're claiming a discrepancy of 44ºK is a 'misrepresentation of fact' they would have you round up to 5000ºK and be done with it.