I often hear about stylist telling clients to switch semi permanent brands because some have metallic dyes in them. I've heard that metallic dyes can cause thinning and breakage. But I have never heard a stylist tell them that the brown is better than the black.
Also if she is using the semi permanent color too often can cause some damage. I think that it would more so be due to protein overloading. That is why it is typically recommended to use after relaxing.
One other thing. The darker the semi permanent dye is the more concentrated it is. Like if you were to use a light blonde versus a black. The blonde semi permanent color would be more gentle on the hair. I think that this could be the reasoning for what the stylist said to your cousin.