The point is that one does not have to modify a system to exhibit uncertainty. You said it yourself: if the particle is in an eigenstate of A, it is not in an e

The point is that one does not have to modify a system to exhibit uncertainty. You said it yourself: if the particle is in an eigenstate of A, it is not in an eigenstate of B. That is, the value of B is fundamentally uncertain, whether or not you thereafter "disturb" the system. Per Wikipedia (not the best source, but accurate here): https://en.wikipedia.org/wiki/Uncertainty_principle https://en.wikipedia.org/wiki/Uncertainty_principle "Historically, the uncertainty principle has been confused[5][6] with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems, that is, without changing something in a system. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.[7] It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems,[8] and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. ... Bohr was compelled to modify his understanding of the uncertainty principle after another thought experiment by Einstein. In 1935, Einstein, Podolsky and Rosen (see EPR paradox) published an analysis of widely separated entangled particles. Measuring one particle, Einstein realized, would alter the probability distribution of the other, yet here the other particle could not possibly be disturbed. This example led Bohr to revise his understanding of the principle, concluding that the uncertainty was not caused by a direct interaction."