Thank you for the dataset.
It appears that the meshes are indeed intersecting, because of this hole on the left side of the head:
I managed to get around this error by selecting a lower number of vertices for the head layer. Select for instance 1082 for the head in the options to generate the BEM surface.
With less vertices, the head surface is smoother and the hole doesn't go as deep into the skull layers, and OpenMEEG accepts the input surfaces.