I've heard the claim that infinite demand for money allows increased supply without triggering inflation, but it's usually used to justify money printing, so that's an interesting idea. However, both sides miss something important when using this argument: The supply of goods and services doesn't change as a result of a higher money supply (although a higher money supply can temporarily drive increased production). The more dollars there are chasing limited goods, the less it is worth.
It doesn't matter if society realizes this is happening, they do understand on some level or another that buying power is falling when prices rise.
You can't really blame banks here though. Fractional reserve banking is, as you say, a natural phenomenon, but, at least so long as there are reserve requirements (either by fiat or necessity--to maintain solvency), private banks can only *multiply* real currency, not mint infinite new currency. The amount of real currency created by central banks directly controls the money supply, therefore, central banks *over the long term* are always to blame for inflation.