The Heisenberg uncertainty principle is tied up with the whole formalism of quantum mechanics. The formalism of quantum mechanics, differential equations and postulates, have never been falsified experimentally up to now, whereas there exist innumerable validations of the theory.
What you were given as a description is misleading and leads to confusions
It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.
The basic equations of QM are wave equations, but not of the usual classical waves where energy varies in space and time. The interpretation of the solutions of the QM equations depend on the postulate that "the square of the wavefunction gives the probability distribution for measuring a given observable". i.e. the probability distribution measured by many single event measurements of the given observable, statistically, is given by the square of the wave function which is the solution of the QM wave equation ( Schrodinger, Klein-Gordon, Dirac) for the given boundary conditions of the problem/experiment.
The word "probability" itself carries uncertainty.
A second postulate of QM is " to every observable there corresponds an operator". These are differentials of some form on the wave function, by space and time variables. In addition, the mathematical construction of the QM equations in terms of operators, i.e. differentiations, introduces pairs of observables that do not commute, i.e. when operating on the wavefunction to get the observables, AB is not equal to BA: this link gives a good outline of how these commutators work. The most well know is the [x,p] commutator and it gives us the standard Heisenberg uncertainty between momentum and position.
So in conclusion, all our data confirm the quantum mechanical view of the microworld and the mathematical theory leads to the uncertainty principles rigorously. No , the HUP is not artifact of measurement but a fact of how nature behaves in the microworld.