You're wrong. When a library is native to some system, it does not mean that it is always shipped with the system. It means that it runs directly, without an interpretation layer in the runtime.
So GTK3 is native to Linux/Xorg. The desktop environment is irrelevant, and may not be based on GTK3.
To put it in practical context, apps built with Gtk generally stand out like sore thumbs on Qt-based desktops like KDE Plasma, both in the way they look and in the way their widgets respond to input. This rather undermines the app's claim "to deliver the best experience" with its choice of UI toolkit.
But if you like, go ahead and believe that I'm wrong instead of trying to understand.
And while it’s true that Qt fits into a GTK desktop better than the reverse, I still find myself preferring using apps written with the toolkit that matches the desktop in both cases.
> Each platform’s native UI toolkit is employed to deliver the best experience
> GTK2, GTK3, ALSA and PulseAudio on Unix systems
If the author is here, please understand that there is no "native" UI toolkit for Linux or BSD. These platforms have several widely-used desktop environments, some of which use the Qt toolkit instead of Gtk.
For what it's worth, Qt is an excellent cross-platform toolkit, and does a far better job than Gtk at looking and feeling native across all the major desktop environments and operating systems. You might consider it instead of Gtk for future work.