Why are the grey matter structures of the inferior medial frontal lobe not directly (not via white matter) connected?
Could anyone offer an explanation as to why these structures are distinctly NOT continuous at this point?


The crista galli physically separates the straight gyrus.


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  ... that would, presumably, permit grey matter from the left hemisphere to be directly continuous with grey matter from the right hemisphere. However, no such connection exists.


They are not physically touching in that location, elsewhere the two hemispheres are not connected (even though physically touching) by gray matter.


  Further, if anyone could confirm whether any part of the cortex exhibits grey-matter-continuity (i.e. not via white matter tracts) between the left and right hemisphere, that would be greatly appreciated.


Except in rare cases, for example agenesis of the corpus callosum (ACC), communication between the hemispheres is via the anterior commissure and the corpus callosum.

The two halves are separated by a deep longitudinal fissure, see this animation: