I don't know if it's that cut and dry. If you study a Operative Systems class or buy a book about them, it'll exclusively deal with the kernel.

Do you not consider Alpine Linux to fall into the general category of "Linux", then? It lacks GNU user space utilities, though there is never a world where I would not consider it a "Linux" operating system. You seem to be overgeneralizing here and making assumptions about OP's intentions that aren't based in fact. I don't see the point in drawing meaningless lines, here. What you're referring to (as described by the GNU project) is GNU/Linux, not "Linux" by itself. The two are often but not always used interchangeably, and treating them as exactly the same leads to major outliers, like Alpine. I've heard plenty of people use the term "Linux" in practice to describe software running on embedded devices that don't contain GNU utilities, so this isn't exclusive to Alpine. In fact, the only real exception that I see consistently to operating systems that run the Linux kernel is Android, so it makes much more sense to formulate a description of the generic term "Linux" as simply having an exception for Android, though I'd argue that the only reasons that Android isn't viewed as "Linux" is because it is a mobile operating system, it is developed with the sole intention of including non-free, proprietary software (AOSP by itself isn't meant to be the full operating system on any device, but rather a framework), and the fact that the structure of the filesystem and the way apps are run differ completely from the ways of traditional "Linux". It seems to be an exception purely by the fact that it operates in fundamentally different ways than other "Linux" operating systems.