This is a false understanding of how the supply and demand for money works. For example, news about QE was positively correlated with long term interest rates. The expectation of an increased future money supply tilted the balance towards the demand side in the present.
Money is fundamentally an intertemporal thing, and we've known since the 1930s that the cute little supply-demand time-slice diagrams in textbooks don't work on the money supply.
Here we see the prices of 10-year bonds falling (=> interest rates rising) with each QE cycle: http://www.pragcap.com/wp-content/uploads/2013/11/arp1.png