That's not right, or at least not nearly the whole story. Of course use of automatic fire is discouraged for situations where it's not effective, such as engaging point targets with aimed accurate fire. For other tasks, the most obvious being suppression, automatic fire can be very effective. Capability of automatic fire was and always has been a requirement driven by the military. For a recent example, look at the U.S. Army requirements for the individual carbine program - selective fire is a requirement for submitted designs.

Anyways, none of this impacts the fact that the term "assault rifle", as introduced with the German Sturmgewehrs and now subverted by the U.S. media to mean "scary looking gun", has a specific military meaning that distinguishes it from other small arms like the battle rifle. Let's use Wikipedia's definition: An assault rifle is a selective fire ... rifle that uses an intermediate cartridge and a detachable magazine.

The distinguishing features of the assault rifle, compared to the contemporary battle rifles at the time it was popularized (like the M1 Garand), is that it is chambered for a lower powered non-pistol cartridge (which translates into lighter weight), has a detachable magazine and is capable of burst or fully automatic fire.

I'm not aware of any military or paramilitary organization that uses a definition substantially different from this, or anything like the one you've suggested.