That's a non sequitur. There is no theoretical mechanism for that statement.
There is a certain quantity of money. If that quantity is not increased, i.e. with inflation, then the rise in price of one commodity will lead to the increased scarcity of that commodity and/or to a lowering of the prices of other commodities and services. With an increasing level of the quantity of money then the average of all prices will rise, though the effect will be uneven. It is economics and it is common sense. As a larger portion of a static money supply must go into one sector of the economy, transportation/fuel perhaps, then there is a smaller portion of the money supply available to all other sectors and their prices will fall.