The LCD only filters light from the backlight. If you don't have a full
spectrum white in the first place the you can't expect decent colour.
White LEDs aren't quite there yet are they?

Absolutely true, except that this particular TV doesn't use white LEDs in
its 'revolutionary' backlighting scheme. It uses small RGB arrays, which
is
why I was questioning whether there was any control over the individual
elements in each array, such that the colour temperature of the nominally
white light that they produce, could be varied. Which would then, of
course,
have a corresponding effect on the displayed colour balance. It just
seemed
to me that given they have gone to the trouble of using RGB arrays, rather
than white LEDs, the reason for that might have been to get a full(er)
spectrum white.

In a very broad sense, the last thing you want is a "full-spectrum" light.
The standard primaries are diluted with too much white as it is.