That’s my favorite viewport clipping hack for retopology. In previous versions of Blender, including the version used for this course, changing the near viewport clipping to 0.01 produced a perfect scenario for retopo visualization. Unfortunately that behavior was changed from 2.77a to 2.8 – here’s my disappointed tweet when I figured it out.
I like this old hack so much that whenever I do retopology, I’ll open my file with Blender 2.77a just to retopo.