The problem is that they think they do. It's a known phenomenon that people rate their understanding of a topic completely independent of their actual expertise. That is to say that ask anyone if they understand a topic and they'll say they do, but when you test them on it, they could be anywhere. The only people whose understanding truly matches their self-evaluations are the experts.
In the field of science, this is exacerbated by the fact that science necessarily uses jargon, and that jargon often overlaps with common language. The term "fragility" in the study of glass-forming materials doesn't mean "it breaks easily", it describes the relationship between the viscosity of the liquid and temperature1.
Some people, like Deepak Chopra, are quacks and frauds who make money by dancing around these misunderstandings, claiming the mantle of science before the public, and then retreating into simple mysticism when challenged by an expert. Seriously, fuck Deepak Chopra. Most of the time, though, it's much more innocent.
Take this, for example. This guy is trying to use QM to prove that a god exists. It doesn't help that Einstein was given to semi-mystical quotes. It also doesn't help that he gets the science wrong, and not just the QM; he gets every day things wrong as well.
For example, he claims that when a tree falls in a forest, it doesn't make a sound. He admits that it makes "air waves", but claims that "sound" is our perception of the event. This isn't a mere quibble over terms. It's a deeper part of both his misunderstanding of QM and central to his "proof".
The problem is the quantum mechanical act of "observation". There's a serious disconnect between the everyday act of observation and that which takes place in the world of QM.
In everyday life, observation is a fundamentally passive event. Information is flying through air all the time and you receive it. Sounds are created, and travel through the air until they reach your ears, at which point your brain interprets them. Light waves travel from a source, bounce off an object, and travel to your eyes, at which point your brain interprets them. At all times, information comes to you absent your effort to retrieve it, and at no time do you actually decide when or how or whether to interpret it. Your brain does that regardless. The human experience of observation is as a passive recipient of some of the vast quantities of information that fill the world around us.
In the realm of the very small, such is not the case. The interactions of the everyday world happen at inconceivable scales; the photons striking your bookcase are so much smaller, that the effect is negligible. But a photon exists on the same scale as an electron. When you observe an electron using a photon, it's like observing a baseball with a baseball bat, like finding a coffee table in a dark room (you know, with your shin). In short, observation in QM is an active event that necessarily impacts (literally) both the object being observed and the object with which you observe. The effect of the one on the other is how you make the observation!
The disconnect, and the reason it allows people to draw false, mystical conclusions, is that the effects are only significant on that small scale, and they're only truly active on that scale. Between the QM world and the world of the everyday, a switch occurs and observation once again becomes a passive event. Newtonian mechanics may only be an approximation, as author Barrier noted, but they're very, very good approximations. Using Newtonian physics, military artillery can fire shells over the horizon, taking into account wind, curvature of the Earth, and the Coriolis effect to not only land the shell but even to set its timer so it explodes precisely and devastatingly above the target. It's an approximation that works in the realm of the everyday.
The act of human observation hasn't been altered or shifted in some way by the discoveries of QM or relativity. When I read a book, it only moves me emotionally. To proceed from QM to the notion that the universe must be observed in order to exist is a non sequitur. The former doesn't lead to the latter. When a tree falls in a forest, it does make a sound, and here's why: In Which I Discuss Shcrödinger's Tired Cat.
1 - If you must know, the ideal relationship is a perfectly straight line when ln(η) is plotted against 1/T. Like many things, viscosity is an exponential function... ideally. In reality, glass-forming liquids deviate from the ideal, and the greater the deviation, the greater the fragility.