"all physical systems are nonlinear"
I think this should not be understood as a hard rule, but as an aphorism that outlines one of the very important differences between theoretical physics and engineering: engineering is supposed to deliver solutions that work in practice, which means not fail catastrophically, which means there is a list of important gotchas, and this is one that you should really remember.
In the context of control engineering, "all systems are nonlinear" makes perfect sense as a rule of thumb, because if you think your system is linear, then your design will fail.
For example, none of your state variables like current, voltage, speed, etc will go to infinity because at some point something will explode or catch fire. What this means is that a system will tend to be linear for small variations of state variables, it will probably follow predictable equations when state variables are constrained inside a certain domain, and have abrupt and sometimes unpredictable transitions between different sets of control laws when certain boundaries are crossed.
For example, above a certain threshold of force, the tires on a vehicle will skid, and that changes the control equations completely. Likewise if some of the wheels lift off the road because you're turning too hard. In these two cases, what changes is not just the control equations, but also the goal and priorities the control system should aim for.
In other words, while it may be true that all quantum mechanical systems are linear, it most likely won't be the first thing to be concerned about if your aircraft stalls and falls towards the ground like a brick.
One of the fundamental differences between theoretical physics and engineering is class action lawsuits... which also are a nonlinear phenomenon, btw.
Note that nonlinearities don't just happen at large state space variable excursions, they can also manifest as small-signal thresholds. For example a motor won't turn at all if there is not enough current to create enough force to overcome friction in the bearing and gears.
So when they say "all physical systems are nonlinear" that's just a colorful way of saying you should always know the limits of your model, you should know when your approximations hold and when they don't, to make sure your design handles transitions between different modes of behavior gracefully and not catastrophically.