I think it was was sound because they (Mashall, et al) could demonstrate that separte was nowhere near equal.
I think it was sound, but I disagree with you on the reason. I don't think the issue was whether separate was equal; I think the issue was that the constitution doesn't allow the creation of different and separate classes of citizens based upon race. The constitution does not recognize race as a barrier to equal protection.
I think it was unfortunate that the focus of Brown was on the separate/unequal aspect rather than equal protection. I think this focus led to some poorly advised forced proactive measures later, such as forced busing, as the whole separate/unequal philosophy moved to its logical conclusion.