Let us say this myopic patient has amplitude of accommodation of 8D. The patient accommodates 8D beyond far point, thus his near point is 1/6+8=0.07m (7.1cm).
If we compare the case with emmetropic eye with accommodation amplitude of 8D, the near point is 1/8=0.12m (12cm).
So, yes, near point of myopic person is different from an emmetropic one. But, you are wrong thinking that near point of "normal" eye is 25cm. The near point is age-and-lens dependent, thus near point is individual one and should be calculated considering amplitude of accommodation.
Look at this picture of age-related accommodation changes -
Look at the scheme of far/near points (near point here is just an example)