Is this different from how the human mind "invents" the color magenta?
Yes, it's a different problem. Magenta requires at least two wavelengths of light, no matter what. Purple, on the other hand can either be red + blue or a single shorter-than-blue wavelength. Computer monitors only have the option of showing purple as red + blue, because there is no "purple" subpixel on a standard RGB display. This article is about how to mix the 3 RGB channels to stimulate your chromophores to simulate the effects of a single-wavelength color.
Edit: I meant "photoreceptors" not "chromophores".