This graph:

http://www.windows.ucar.edu/tour/lin....html&edu=high

Shows the density of water as a function of depth. Water density changes
from 1.025 gm/cm^3 to 1.026 gm/cm^3 in 250 feet. That's a change of 0.1% in
250 ft. Since that portion of the curve is linear, one can estimate that
water density would change .0004% over the diameter (tip to tip) of a 12
inch propeller. So is a .0004% change in water density (in the vertical
plane no less) going to walk a boat sideways? Don't think so.

Now if the propeller shaft mounted off centerline reduces the walk, this
would indicate that sideways (lateral) thrust from the propeller directed
against the hull is a factor. Also with the shaft off center the boat is
less likely to "torque" against the propeller. It's always good to find
physical evidence to support a conjecture.