In Brain-Computer Interfaces (BCI), measurements of the users brain activity are classified into commands for the computer. With EEG-based BCIs, the origins of the classified phenomena are often considered to be spatially localized in the cortical volume and mixed in the EEG. Does the reconstruction of the source activities in the volume help in building more accurate BCIs? The answer remains inconclusive despite previous work. In this paper, we study the question by contrasting the physiology-driven source reconstruction with data-driven representations obtained by statistical machine learning. Our analysis suggests that accuracy improvement from physiological source reconstruction in BCI may be expected mainly when machine learning cannot be used or where it produces suboptimal models. However, we argue that despite the use of physiology-based source reconstruction, data-driven techniques remain necessary to attain accurate BCI systems. Finally, we observe that many difficulties of the surface EEG classification remain challenges in the reconstructed volume.