I don't know if all the cells in your eye are perfectly tuned to three peeks. I expect biological systems to show some variance.

The mechanism is chemical/physical, though, and depends on the absorption spectrum of a certain pigment molecule for each type of receptor. I strongly suspect the variance in those is likely to be tiny.

The fact that you can see a full spectrum -- as in a rainbow, thin-film refraction on a puddle on a paved street, etc. -- should be an indication that the band-pass for neural firing is relatively wide. If each optical receptor had a narrow acceptance window (the way that individual atoms absorb), there would be gaps in the rainbow. Remember that ALL of the colours you see in a rainbow are pure, composed entirely of photons of a particular wavelength proper to each of those colours. It's not RGB; it's not CMYK.

We can, to an extent, simulate a full spectrum through additive and subtractive colour mixing of "primaries", but it is only a simulation. (And Edwin Land demonstrated that we don't actually need all three of R, G and B in order to create the illusion of a full-colour picture with only a comparatively tiny gamut loss. It is a fragile thing, though, and requires the integrative function and cognitive mapping of our brains.

Similarly, we can easily tell the difference between full-spectrum lighting and discontinuous spectrum lighting. Discontinuous spectrum lighting makes us uncomfortable. None of the colours looks quite right. Food is unappetizing, pictures and people less attractive. Did the light-makers just miss the right mix of frequencies by a hair? No -- any scheme that relies on a small number of discreet wwavelengths will cause a similar discomfort. We may not know why we feels the way we feel at the time, but we sho' 'nuff knows we'se feelin' it.

You make a good point - I forgot about indirect light and banded spectra interacting with surfaces.