NO RGB LED is full spectrum. They have narrow peaks in Red, Green and Blue to match the peaks in our RGB colour perception, so colours can be simulated as they are on TV or monitor or phone screen. Colour displays are trick.
If you illuminate real world objects purely by R G B LEDs some colours are wrong and some are dark. White CFL, CCFL and "White" LEDs use a mix of phosphors. Unlike real LED chips without phosphor, a phosphor has a broader spectrum. A mix can provide good colour rendition for illumination of a room. This can be unconnected to Colour Temperature! You can get any Colour Temperature from R, G & B LED light combined.
https://en.wikipedia.org/wiki/Color_rendering_index
ALL "white" LEDs are really blue, violet or near UV. The R G B LEDs never have a phosphor as that would reduce the output. The blue LED chip in an R G B package is chosen to be closer to the eye's blue peak. A blue LED chip for a white LED uses a mainly yellow phosphor mix (other colours included) will ideally be shorter wavelength to be more efficient producing the Red to Green part of the spectrum via the yellow phosphor. Very cheap white LED lighting can lack the Cyan part of the spectrum, so illuminated cyan objects will look greener, bluer or darker or even grey!
We are far more sensitive to hue than brightness or saturation.