Assume that corn is identical across all countries, and is freely traded with zero transportation costs. We then know that "the law of one price" will hold for corn. The price of corn in Canada will be the same as the price of corn in the rest of the world.
Why? Suppose it weren't. First suppose the price of corn were higher in Canada than in the rest of the world. Then Canada would import all its corn, and there would be an excess supply of corn in Canada, and the price of corn in Canada would fall. Or suppose the price of corn were lower in Canada than in the rest of the world. Then Canada would export all its corn, and there would be an excess demand for corn in Canada, and the price of corn in Canada would rise.
That second paragraph is perhaps obvious, but it is not redundant. It explains why the law of one price holds.
Now suppose Canada discovers an extra ton of gold. What happens? Our model tells us that the new equilibrium looks exactly the same as the old. That whole ton of gold flows abroad. (Please do not argue with the model, because that is not the point of this post.)
But what is the mechanism that causes that extra ton of gold to flow abroad?
There are two stories we could tell:
1. David Hume's price-specie flow mechanism. The extra ton of gold causes the Canadian price of corn to rise above the world price, which causes Canada to import corn in exchange for gold, so the gold flows out of Canada.
2. The real balance mechanism. The extra ton of gold means there is an excess supply of gold in Canada, which causes Canadians to demand more corn, and since Canadian producers don't want to supply more corn, the extra corn is imported in exchange for gold, so the gold flows out of Canada.
The point of this post is that we cannot say that one of these two stories is right and the other is wrong. Neither is right, and neither is wrong. We need both stories; they are complements not substitutes. Someone who asserted that the first story is wrong because the law of one price always holds would be asserting that the second paragraph in this post is wrong, and that we do not need to explain why the law of one price holds. If you deleted that first story, how would you answer someone who said the second story is wrong, because the excess supply of gold and excess demand for corn in Canada would simply cause the Canadian price of corn to rise?
This is not an empirical question. The truth of the model is an empirical question, and the truth of each equilibrium condition is an empirical question. But someone who explains why the law of one price holds by explaining what would happen hypothetically if it did not hold is not asserting that sometimes it does not hold. If I explain why water in the lake has the same level everywhere by supposing it were higher in the North than South and saying it would then flow downhill from North to South you do not falsify my explanation by showing there is no empirical evidence it ever was higher in the North than in the South. I am explaining why there is no empirical evidence it ever was higher in the North than in the South.
The two stories of the transmission mechanism reflect the two equilibrium conditions. The first story assumes that the second equilibrium condition always holds, and explains why the first equilibrium condition holds. The second story assumes that the first equilibrium condition always holds, and explains why the second equilibrium condition holds.
That simple model had two equilibrium conditions and two stories of the transmission mechanism. In a model with n equilibrium conditions there would be n stories of the transmission mechanism. Or more than n, if you combined them. How many equilibrium conditions are there in the real world?
There are not two competing theories of the monetary transmission mechanism in that very simple model. There is no such thing as the monetary transmission mechanism. A "transmission mechanism" is not a causal chain; it is an explanation of why one equilibrium condition holds. The search for the transmission mechanism is a snipe hunt beloved by the people of the concrete steppes. It's a form of category mistake, like searching for which building on campus is the university.