I think you have it right. Inflation in general is a monetary phenomena. Too much money chasing too few goods. Thus restricting growth does not in and of itself slow inflation. Declining growth can reduce inflation, but that is because the velocity of money can fall, basically because lending is reduced. Obviously this is a poor trade. Lower growth to combat inflation. Rapid growth not fueled by increasing the money supply, either through reserve creation or by increasing leverage, does reduce inflation. Same amount of money chasing more goods means lower prices.

Of course a particular area suffering from inflation, such as food, can increase due to lack of supply. As you point out, decreasing trade does not help that at all. It just reduces the total supply of goods, and thus can fuel inflation generally.

Here in the US we are seeing how a slowing economy is increasing inflationary pressures, even as we face the possibility of deflation. Slowing growth combined with a falling dollar is pressuring food and import prices. Meanwhile, deflation is hitting asset prices such as housing. All things being equal, if asset prices fall consumer goods prices should rise. The kicker is that the debt crisis may end up crushing credit creation, leading to a decline in the velocity of money severe enough to cause outright deflation down the road. Scylla and charibdas.