Let me borrow a term coined by Cecchetti, who calls this the “accounting” theory of inflation. The problem arise because prices affected by trade are “relative” prices. The import of a foreign product that is cheaper than the domestic one produces a change between this price and the other prices in the economy, while inflation is actually the aggregate change in general nominal prices.
what is fallacious is to take these two notions the same way. This is better appreciated when taking into account that, by definition, when the relative price of a certain good falls, there should be a rise in the price of the other goods against which it is compared.