This notion is based on SLA Marshall's work, and his methodology is extremely suspect. He has been accused of being a fantasist, and either twisting the facts or outright inventing them to suit.

I've heard this several times: that the rate of death in many wars is much lower than it should have been considering the level of skill of the combatants, the accuracy of the weapons and the rate at which they fired.

This is an interesting idea, but it makes me wonder, how does one know what the rate of death should have been? Equally puzzling when one considers wars where small arms and other individually-aimed weapons at human targets are not the main causes of death.

I am aware that there's some statistic about Vietnam, where the number of bullets per kill was in the thousands, but in that case I am under the impression that factors like extensive suppressive fire and the difficulty of actually hitting a target in dense jungle environments would skew that.

This is perfectly normal for any war. Countries have literally millions of rounds of small arms ammunition in storage ready to use. Combat accuracy, discounting rounds used for suppressive fire or recon by fire and other associated uses, is not very good due to a great many factors which complicate the process (e.g. excitement, poor visibility, poor light conditions, a moving and/or indistinct target, etc).

As /u/flyiceplick pointed out, the idea is partially based of military historian SLA Marshall and popularized by the book On Killing by Dave Grossman. While Marshall's research methodology has been questioned, Grossman uses a variety of sources to further back up the claim that killing is inherently difficult, I suggest reading the book if you want to fully grasp the argument, but I can run down some of the bullet points.

As a quick note, Grossman also argues that the human aversion to killing has been largely overcome in certain military forces due to the type of training adopted after WWII to counter these problems (whether or not they had been blown out of proportion.) By the Vietnam war, even Grossman argues that most soldiers are actually aiming at people, firing at them, and killing them. So Vietnam is actually excluded from this analysis.

On to the main argument, Grossman focuses on the idea of posturing and violence versus actually killing. Most animals will fight for dominance within their species, but rarely actually kill each other (excluding some species which will eat babies.) Early human warfare seems to mimic this pattern, with war being violent but not necessarily very deadly. Large scale death during war either occurred after the fighting was actually over (during an opposing armies retreat or after a town fell) or outside of the battle (lack of supplies or disease.) Its hard to tell how accurate this because classical sources almost always exaggerate the size and deadliness of ancient battles. There are definitly some exception to this rule that are fully agreed upon though (Battle of Canae springs to mind) so take the idea that ancient warfare was little more then a deadly sport with a grain of salt.

Still, there are definite examples of warfare being disconnected from death that occurred in later eras. Italian mercenaries, for example, were famous for fighting without really killing each other.

Grossman goes on to support this idea by looking at battles with gunpowder. He compares accuracy rates on the battle field with muskets and rifles against Prussian tests done on training ranges that suggest that most soldiers didn't really aim at the enemy, either aiming high, low, or not firing. While test conditions are obviously different from battlefield conditions, the Prussian test did show effective range dropped by like 30 yards and accuracy plummeted on battlefields, way more than you would expect (I don't have exact numbers since I don't have the book with me.) The exception to this rule is artillery, since indirect fire is much easier psychological (in the framework of this argument.)

Grossman uses Marshall's work to show that this trend continued into WWII, basically saying that unless a solider is trained in a certain way, most humans (he says 90% but doesn't really give a rational for that specific number) will not kill someone who they are looking at face to face.

Not saying he's right, but there are a bunch more facts that do at least partially support this idea if you are interested.