The 'parallel' he is talking about is a machinists set up tool. It's a rectangular bar of steel with precisely parallel edges and faces. Normally it is also ground very smooth.
Laying the indicator tip against that smooth face is easier than trying to get it to hit the knife edge. That's all.
You are right, TDC is irrelevant. What IS relevant is that the relationship (angle and distance) between the cutters and the indicator tip not change between measurements.
Bill