That's a step forward: at least now we have a rough idea of where the cause lies.
I have tried copying the default terrain as a second layer over the JMS terrain. The upper portion of the JMS terrain (the one you replaced) appears to be shifted upwards by a single pixel, even though this is the only difference I manage to detect (I might have missed something else).
In the image below I have set the transparency of the default terrain to 30% and the two images clearly do not match.
I have no clear idea as to why this affects the AI behaviour: my best guess is that the shift makes the road not- functional and so the river hexes remain impassable. You could test this by moving a unit along a road and by checking if it gains the +1 hex bonus.
