Most folks don't understand what Physicists mean when they say "Reality doesn't exist at the Quantum level". Words like "Reality", "Illusion" etc. mean quite different things when applied at quantum level vs. classical-macro level.

The best book to get a grasp on the above is Werner Heisenberg's classic Physics and Philosophy: The Revolution in Modern Science. The introduction by Paul Davies itself is worth the price of the book since it highlights the main issues quite clearly.

At the fundamental level quantum systems have an inherent indeterminism (as a consequence of the famous uncertainty principle) which is what we find hard to grasp. It does not mean total anarchy but that you can only calculate relative probabilities of the alternatives in the answer set i.e. it is a statistical theory. Thus it can make definite predictions about sets of identical systems but generally cannot say anything definite about a specific individual system.

For example, an electron doesn't exist as a single thing occupying a specific trajectory around the nucleus. It only exists as a set of potentialities occupying an area of space viz. the so called electron shell. Only when a measurement is made does a electron-with-position or electron-with-momentum can be said to come into existence (since before the measurement there are only probabilities and you cannot measure both position and momentum sharply simultaneously). It is in this sense that the Reality of an electron is said to only exist in the Measurement/Observation and cannot be said to exist otherwise.

The other side of the coin is that, Modern Neuroscience tells us that the Brain itself is wired to Construct Reality from incomplete data and we seek/construct patterns where there are none. See for example Cordelia Fine's A Mind of Its Own: How Your Brain Distorts and Deceives and watch this Ted talk by Susana Martinez-Conde Reality is made of illusions—and we need them - https://www.youtube.com/watch?v=FzDw07RqCSs