After stereo image rectification, why does the relation between disparity and depth still apply?
Image rectification does not make this assumption valid.


Yes it does! 

From the wiki: https://en.wikipedia.org/wiki/Image_rectification


  Image rectification warps both images such that they appear as if they have been taken with only a horizontal displacement and as a consequence all epipolar lines are horizontal.


The term can be used in an overloaded manner though, by instead implying that projective distortions from the camera are removed. So you have to be careful.