Neutral axis coincides with the centroidal axis only in the region of linear stress - strain curve. 
In WSM, we use linear stress-strain curve, while in LSM, we use non linear stress strain curve, hence in LSM, centroidal axis and neutral axis do not coincide. 
Hence assertion is correct.
In working stress method, there is strain compatibility in bond between steel and concrete and it is assumed that concrete is elastic, steel and concrete act together elastically and the relationship between stress and strain is linear. Hence reason given is wrong.