Recently, a number of articles have argued that deep learning models such as GPT could also capture key aspects of language processing in the human mind and brain. However, I will argue that these models are not suitable as neural models of human language. Firstly, because they fail on fundamental boundary conditions, such as the amount of learning they require. This would in fact imply that the mechanisms of GPT and brain language processing are fundamentally different. Secondly, because they do not possess the logistics of access needed for compositional and productive human language processing. Neural architectures could possess logistics of access based on small-world like network structures, in which processing does not consist of symbol manipulation but of controlling the flow of activation. In this view, two complementary approaches would be needed to investigate the relation between brain and cognition. Investigating learning methods could reveal how 'learned cognition' as found in deep learning could develop in the brain. However, neural architectures with logistics of access should also be developed to account for 'productive cognition' as required for natural or artificial human language processing. Later on, these approaches could perhaps be combined to see how such architectures could develop by learning and development from a simpler basis.