It doesn’t preclude it correct, however it provides a pretty strong examples of where reductionism is lacking, which what I believe has turned a lot of philosophers of science against pure reductionism (I am probably oversimplifying here. An expert science historian [which I am not] could probably write a whole book about why reductionism is not as popular today as it was in the 1970s).

There are a whole lot more physical processes going on in our bodies then just neural activity. And my best guess is that is exactly where reductionism fails. It is possible that neural activity is a necessary but not sufficient condition for consciousness. It is also possible that we are looking in the wrong direction, that consciousness arises via interactions with the world. In either case (of which I find the former quite convincing) we will never be able to describe the mind by just looking at neural activity.

I am actually of the opinion that cognitive scientists are doing an excellent job describing the mind with our current theoretical models which excludes the tough questions of consciousness.