Actually? Probably yes. Every member of the military I've spoken with emphasizes that their training explicitly discourages the use of fully automatic fire. Real life isn't like Call of Duty. Special Forces operators don't go in flinging grenades left and right, blazing away with full auto fire from the hip. Doing so is both a waste of ammunition and a danger to one's allies.
That said, though, I find the distinction between "assault" and "regular" rifles to be quite silly. In practice, "assault" tends to mean "it has a rail for attachments and looks scary", just like "sniper rifle" tends to mean "rifle with a scope". In both cases, the essential portion of the definition is does not have anything to do with the gun, but more to do with the person carrying it. A sniper rifle is a rifle carried by a sniper. Even a relatively weak .22LR can be a sniper rifle in sufficiently skilled hands. Similarly, an assault rifle is a rifle carried by someone with assault training.
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.
While you're right in that the person doing the shooting is far more important than the weapon, it's pretty clear that some weapons, like fully-automatic shotguns, are designed for specific use cases. You wouldn't use a .50 Barret to hunt deer, and you wouldn't take a micro Uzi to the practical range.
Drawing a line between civilian and military use suitability is difficult, but that doesn't mean there is no difference. That's why there is no assault rifle law in the US, but rather some features of weapons have been banned from private use.
To be accurate, there are no weapons features that have been banned from private ownership and use in the U.S. at the federal level. Certain weapons fall under regulation of the National Firearms Act and require payment of a tax before transfer. Examples are machine guns, suppressors, destructive devices and short barreled rifles/shotguns. These are all legal to own by individuals at the federal level.
A few states do outlaw or ban some specific NFA weapons however - for instance 5 states outlaw individuals from possesing machine guns.
An assault rifle is a step down from a battle rifle. A battle rifle fires full sized .30 caliber rounds, an M-16 would be an assault rifle. Smaller cartridges than a battle rifle.
Are you suggesting the US government asked google to stop runnings ads for knives?
In the same country where I can pick up a semi automatic assault rifle at WalMart?