Exactly right. The rules of quantum mechanics are in their essence not much more complicated than high school algebra. It is the logical consequences of those rules that are hard to wrap your brain around.
Go read a book on number theory some time. It looks hard too. But it is about nothing more than the properties of the natural numbers, which any grade schooler can understand.
Likewise, QM looks hard, but at its core it is little more than linear algebra, which any high-school math student can (or at least should be able to) understand.