The article was about excess money, not inflation, but those are questions worth exploring.
In the existing paradigm, once money is created it is in the (global) economy forever. The existence of inflation in itself creates a demand for money over and above any other demand there might be for it. The question becomes whether the central bank/central government partnership can withstand the pressure to allow more money to be available in the economy, thereby feeding the inflationary beast, creating more pressure for more money, etc., etc.
To fight inflation money must be taken out of circulation. In the existing paradigm that would require two things: banking systems must capture money and hold onto it and governments must run a surplus. Even investing in public goods and services keeps money circulating in the economy, feeding inflation.
Monopolies keep supply smaller than it would be in a competitive market, which keeps prices higher than they would be with a competitive market. Likewise, in an inflationary environment they are freer to raise prices than companies in a competitive market would be. So they are always contributing to higher prices.
Price inflation, though, is a trend of increasing prices in general. So the existence of monopolies does not create price inflation--those higher prices they create could be stable, not increasing--but their existence does exacerbate inflation by making increasing prices easier.
In the paradigm I have developed excess money is regularly drawn out of the economy altogether. Whether it reenters the economy is a matter of demographics, and nothing else. I hesitate to say inflation could ever be an impossibility, but that is the only reason I'm not saying that it would be an impossibility with that paradigm in place.