Correct, MNT is used extensively and even though satellite technologies are slowly being relied upon more and more to allow for distance based longitudinal separation rather than time based, my oceanic area in particular will always assign a mach number to aircraft entering.
That link you provided clarifies the confusion. As a controller, I just assign a Mach and the pilot does what they do to comply. It sounds as though most modern aircraft will have the indicated mach shown to the pilot be the actual true mach. Some aircraft however will require the pilots to do the conversion. That makes sense because if we were to profile an aircraft for knots instead of mach, we use true and not indicated.