> From what I understand, a modern monitor is capable of displaying the entire range of colors perceptible to the human eye. Am I mistaken about that?
It kinda depends on what you think as a color. Computer monitors rely heavily on that (normal) human vision can not distinguish from eg. red-green and "true"[1] yellow, even though they are completely different from physical perspective. So a typical computer monitor does not bother to create "true" yellow and instead cheats by outputting red-green when asked for yellow.
If we had an hypothetical tetrachromat with additional cones sensitive for yellow light, her color vision would span the same range as normal (trichromat) color vision, ie cover the same piece of EM spectrum. But normal computer monitors would not be able to reproduce for her what she sees in real world.
Then there is the somewhat related discussion about violet and red-blue which is quite curious when you begin think about it.
[1] I'm using "true" color to refer light with specific wavelength