> The Uncertainty is not due to finite information. It is an inherent property!

That's what they said, though? Although I suppose it could stand to be emphasized more:

Physical quantities that have an uncertainty principle, such as position and momentum, are inherently related to each other by a Fourier transform. At a quantum-mechanical level, position is the Fourier transform of momentum, and vice versa - anything that constrains the position to a narrow interval (including but not limited to measuring it very precisely) inherently also smears momentum over a wide range of possibilities, even it was itself previously tighly constained (and, again, vice versa).