the brain interprets the wave spectrum which, yes, really exists.
Exactly. Our brain interprets it but color really does exist.
You can really screw with people if you tell them that leaves are every color but green.
In my courses I call this a "conscious fiction": it is in our conscious mind (and in some people's dreams), but it is a fiction because while the electromagnetic waves exist, our "narrative" about them (that they are separate colors) does not exist at a physical level.
As a (Lutheran) Christian, I would assert that the experience of light waves as color is a gift from God, on at least two counts: it allows us a more nuanced view of physical existence (we see objects more effectively because of the experience of separate colors) and simultaneously provides aesthetic pleasure--as I type this I am watching a couple of white herons walking through my green back yard, below brown and green trees pointing to a blue sky.
Of course you are correct. An objective fact - a repeatable and uniform observation.