We consider the almost disturbance decoupling problem (ADDP) and/or almost D-bounded disturbance decoupling problem ((ADDP)(D)) with internal stability for linear systems subject to input saturation and input-additive disturbance via linear static state feedback. We show that the almost D-bounded disturbance decoupling problem with local asymptotic stability ((ADDP/LAS)(D)) is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable, no matter where the poles of the open-loop system are, and the locations of these poles play a role only in the solution of (ADDP/GAS)(D), (ADDP/SGAS)(D) or ADDP/GAS where semi-global or global asymptotic stability is required.