Violet is a true wavelength, and does occur in nature.
Magenta, formed by mixing red and blue, does not exist in nature. For that reason, "magic pink" (full-brightness magenta, #ff00ff) is often used as a transparency color when the image format does not support an alpha channel (e.g., sprite sheets, Winamp skins).
It's not true to say that mixtures of red and blue 'do not exist in nature'. Fuchsia petals really are that color. All you need is a substance that preferentially absorbs green wavelengths but reflects reds and blues.
What 'does not exist in nature' is a single wavelength that produces the equivalent stimulation of your L, M and S cone cells as a mixture of red and blue light does.
But most of what we see in nature is not single wavelength light - it's broad spectrum white light reflecting off things with absorption spectra.
The reason stuff looks so weird under certain LED lights or pure sodium light is that the source light isn't broad spectrum - it's missing wavelengths already - so the way it interacts with absorption spectra is unintuitive. Something that looks blue under white light should still look blue under blue light - but a blue LED might just be emitting blue frequencies that the object absorbs, so it looks black instead.
Magenta, formed by mixing red and blue, does not exist in nature. For that reason, "magic pink" (full-brightness magenta, #ff00ff) is often used as a transparency color when the image format does not support an alpha channel (e.g., sprite sheets, Winamp skins).