Excellent! So this claim was wrong?
The real problem with the US$ as a reserve currency is that whenever the US government has been running a bit short it just prints some more.
As you have already stated, inflation is caused when "whoever increases the volume of money and credit relative to available goods and services." The whoever list is really very very short, like a club with one member whose name dare not be uttered in this circles. When the $ is a world reserve currency it is held by other central banks who loosely or tightly peg the value of their own currency to the dollar. Therefore when an extra dollar is created it inflates the world's economy, and the extra demand is on the world-wide economy. When on the other hand the $ is on par with an Argentinian peso, then, the exchange rate on the American peso drops relative to the world currency, ceteris paribus , and you now only steal from US citizens.
Now tell me. What happens when you take advantage of the fact that the $ is the reserve currency for 40 years by printing lots and lots of it and having it purchased by central banks around the world, and suddenly one day they wake up and decide they are holding, collectively enough of it?