The ArcPy Stretch function does not honor the stretch type or rendering parameters over a raster object.

Workaround

1. Select the resulting raster datasets manually and change the Stretch Type drop-down menu from the default (standard deviation) to the one defined previously in the ArcPy Stretch raster function. 
2. Adjust the other parameters such as Dynamic Range Adjustment (DRA) or Gamma factor manually. 

Steps to Reproduce