There's this really common explanation for Heisenberg's Uncertainty Principle, but I quote it from Classical Dynamics by Marion and Thornton:
The wave character of the photon precludes an exact measurement, and we can determine the position of an electron only within some uncertainty $\Delta x$ related to the wavelength of the photon. By the very act of measurement, however, we have induced a change in the state of the electron, because the scattering of the photon imparts momentum to the electron.
And then the author continues to talk about the definition of the Uncertainty Principle. Now if the given explanation is correct, doesn't it mean that these uncertainties originate from our inability to measure it precisely due to the photon scattering? If so, this has nothing to do with the intrinsic probability of an electron existing in a particular state and it can only be in one state at a time. How,then, is the Uncertainty Principle known to be a fundamental physical law? Where is my understanding incorrect?(I hope I have been clear with what I wish to convey).
