I mention 'small deflection' because the linear solution would exactly match the hand calculation. In a linear solution, the tip of the cantilever is always the same distance from the support no matter how large the deflection. Once you turn on large deflection, the solution includes nonlinear geometry deformations. With a thin cantilever and a large force, the beam can deflect enough to foreshorten significantly and the distance from the supports to the force is no longer the same dimension it was at the beginning. This will be true for either Deformable or Rigid. With Deformable, the location of the force may end up in a slightly different location than it did for Rigid.
In a linear solution, if you double the force, the tip just goes straight down twice as far. In the nonlinear solution, if you double the force, the tip moves further in the -X direction, changing the reaction force.