Thanks for the kind words, Allen!
Let me try to explain more carefully here. By using a better pipette, you would reduce the uncertainty. However, that uncertainty has not vanished - it has been concentrated near the point estimate. Like sand under a carpet, we can only move the sand around, and never remove it. Better measurements / more data move it (usually) to create a taller peak. However, there is the same uncertainty, just at a smaller scale. Graphically:
