At ~2:57, you say you're turning on clipping and then select all and get independent/mirrored movement of each quad of the cube. But you're not selecting "clipping" in the modifier properties. How are you doing this, because I can't get it to work like you're demonstrating?
Hi Jon, @jlampel says he is going to turn on Clipping at ~2:57, but he actually turns it on at ~3:16. He is first demonstrating what happens if you don't turn on Clipping.
I hope this clears up the confusion a bit for you..., if not do not hesitate to ask..
Ah, I see what I was missing now. I was confused about how you were getting the four quadrants to move independently, and it's because you had the cursor snapped to the selected quadrant prior to turning on clipping. This was not the default behavior or placement of the cursor.