I think you and the other person are referring to two different "spectrums". Our vision covers a tiny portion of the EM spectrum, for instance, we can't see infrared, microwave, gamma, x-ray, etc.
There are separately colors which we are wired to hypothetically receive, as you point out (and I find interesting) - IE, if you replace the eye with some sort of artificial replacement, then such a signal could get received by the brain, but with the current sensors it is impossible (also, I suppose a colorblind person could receive such a signal as 100% red without the other colors).
There's also the possibility during a dream of creating objects or sensations that are not physically possible. For instance, I've had dreams where I had a form of telekinesis, and obviously there's no sort of brain wiring to manipulate physical objects outside of the normal motor functions. Still, it made sense in the dream - and it's not like I could describe how I did it, and it's not because the hardware exists but the sensor doesn't.
Although - you could argue that there's a layer of abstraction in the brain of such things in the brain - for instance, when I'm typing these words I don't actually ever have any conscious awareness of my finger motions. I don't even think about the act of typing at all; only the words. So, thinking about it, the brain does have an idea of manipulating objects outside of a need for muscles to do it.
I would think for a tetrachromat the abstract sensation of seeing colors you can't describe to others is itself a familiar one, and that feeling itself is something you might encounter in dreams. My dreams tend to start with a feeling, and then build a context for it.
Tl;dr - dreams are weird.