Another thing to consider is the solute potential of material left in the rock. Even injecting sea water, if there are water soluble compounds (sulfur, acids, iron, etc.) in the field the water activity will want to equilibrate. Water will flow from a dilute solution to a concentrated solution until the concentration of solutes is balanced or the sources migrate away from the rock.

Plants grow through this mechanism. They raise the solute potential in cells (using any small molecule, salts, sugars, acids, proteins, etc), water flows in from outside, raising the internal pressure and forces the cell walls to physically deform/stretch in one direction along a fault zone in the cell walls. The power of osmotic potential can be very large, getting into the 1000's of PSI. Plant roots break granite rocks apart using this mechanism as they grow. I am not saying this mechanism is happening in this field, just that it shouldn't be discounted in a water drive oil field.