That's not entirely accurate. The term 'full spectrum' is best contrasted against what is not considered full spectrum. On one end, we have actinic type bulbs that emit almost exclusively high wavelength blue light. At the other (and most notably) we have incandescent bulbs. They emit red orange-red light, but much of their light is in the infrared region where neither we nor plants can see it. 'Full Spectrum' describes any bulb that emits in the entire visible spectrum, which includes most fluorescent bulbs, including 6700K, 5000K, 4000K, but also 10000K, 12000K, 18000K, and colormax.
What's interesting is that plants CAN USE actinic light. They usually emit something like 40-60% of the PAR of traditional plant-friendly bulbs, but that's still usable light energy. What's more interesting is that when people stuck PAR meters under different temperature bulbs (IE, this is actual data and not speculation), they found that the difference between 10000K bulbs and 6700K bulbs was trivial between the same manufacturers. What's more, in another instance, someone found that the 10000K bulbs actually put out MORE PAR than 6700K.
What does this tell us about color temp? It means that it's only really important when you're trying to decide what color looks best to YOU. To say that 6700K bulbs are ideal for plants or that 4000K bulbs are most like the sun is mostly just hot air. The color temperature is only a measure of what we can see. Think about it like this: you're listening to an accomplished symphonic band playing Beethoven, and during a particular spot, violins have the melody. To say that any bulb is to be judged by it's color is to say that the symphony is made entirely of violins, when in fact the entire symphony playing is playing together. You may prefer a strong cello line, or a rousing trumpet part, but either way the entire orchestra is 95% the same, and is what matters.
