I work in neuroscience and I don’t agree that it is on much firmer ground that psychology. In fact, as some people in the community have noted, the neuroscience mainstream is probably still in the pre-paradigmitic stage (using Kuhn). And believe it or not, a lot of neuroscientists naively do believe that the brain is like a computer (maybe not exactly one, but very close).
That’s fine, I don’t think you’re being an ass at all. Brette is saying that just because there is a correspondence between the measured spike signals and the presented stimuli, that does not qualify the measured signals to be a representation. In order for it to be a representation, it also needs a feature of abstraction. The relation between an image and neural firing depends on auditory context, visual context, behavioural context, it changes over time, and imperceptible pixel changes to the image also substantially alters neural firing. According to Brette, there is little left of the concept of neural representation once you take into account all of this and you’re better off calling it a neural correlate.