That explanation, though, is non-canonical. Which I'm glad of, because I find it highly counter-intuitive; why would the Andorians name the world they're actually from the diminutive of the gas giant it happens to orbit? The ancient Andorians wouldn't have known that their world was orbiting the gas giant; they probably would have thought the gas giant was orbiting their world, the way Humans used to think the Sun revolved around Earth.
I agree with what you said, though this part made me think. I wonder if the gas giant would actually dominate the sky in the way our Sun (or the Andorian sun) wouldn't. I don't feel like doing the math to find out just how large a difference there would be, but I imagine the gas giant would be much larger in the sky than the star. So perhaps the "Andor-centric" viewpoint might not have been the same as on Earth?