Your textbook is pretty dumb. it's just as much linux as your wireless router is probably linux - no, it's even more so linux than that. just because you're not using X doesnt make it non-linux - or then me and my brothers first linux installations weren't linux too(they were).
Android most definitely is Linux. you cannot separate the two. even if you're not using ndk and using only dalvik/art, you're still using linux threads and a bunch of other linux things almost directly.
you COULD maybe run "android apps" inside another operating system, but Android as in lets say android 5.0 or whatever is definitely linux and a lot of how the apps and systems on it work bind directly to the linux kernel all the way to the way process security works. furthermore you can just run linux binaries too, provided that the linux installation of course on the phone has everything that binary needs in order to run.
anyways, if your android textbook says it's not linux, then people who learn by it will probably never even think that it is linux and thus can just wonder with amazement at what some apps do while they can never make their apps do the same.
did the textbook also tell you that asynctasks are somehow magical without showing you the source to them, disproving them as magical and making them look like a dumb waste of space?