The price of gold might have remained constant, but that's hardly the binding factor here. All inflation is measured with respect to a basket of goods and if you choose "an ounce of gold" as your basket of goods then under a gold standard you'll get 0 inflation by definition.
Exactly. If you define a new basket of goods to be "one bottle of coca-cola" (let's call it's a "Coka"), then there has been no inflation since coke was first sold! One bottle of coke still costs the same as 1 Coka!
I am reminded of The Economist's "Big Mac Index", comparing currencies' purchasing power to buy a Big Mac in different countries. The index "seeks to make exchange-rate theory a bit more digestible". ;)