No, you can photograph the CC under any illuminant. The instructions you're referring to only applies to the case where you've specified that you want to use the Chart Wizard feature __only__ to build 6500 K corrections (i.e., you choose 6500 K from the popup menu in the Chart tab).
For your case, when you're building a profile for 4800 K, choose "Both Color Tables" from the profile menu popup and it will work fine.
Regarding the error: the DNG Profile Editor checks all gray patches to see if they are relatively free of color casts. This is a sanity check. There are 3 possible reasons you might be getting the error: (1) you really do have a color cast, in which case reshoot your target carefully or (2) your image is very noisy (should try using low ISO to shoot the CC), or (3) maybe you didn't position the 4 markers appropriately to identify the 4 color patches?