In other words, they're trying to answer the question of whether you and I are perceiving the same thing in our brains when we look at something that we both agree is "red"?
Sort of, but it depends on what you mean by "perceive".
They are measuring responses in the visual cortex. What you feel about that is likely also similar to most people but I bet it's another layer in the brain doing that connection.
They are obviously not. Your representation of red is based on your experiences and mine is based on my experiences.
Experience but also biology. Blood is red and some people faint at the sight of blood, that can't be all attributed to experience.
Mabye it is a trait that we are predisposed to learn.
But I doubt it is part of the default neural network as it is encoded by the genes.
Many of us are colour blind which confirms we're definitely not all perceiving the same thing...