> The US had emitted lots of money and has very little inflation.

Are we talking about quantitative easing here?  Quantitative easing has caused inflation, just not consumer price inflation.  Look at stock prices, which are about 50% overvalued according to some well regarded investors (e.g. [Warren Buffett](http://investcorrectly.com/20141126/us-market-overvalued-buffett-indicator-market-cap-us-gnp/)).  

A common complaint about quantitative easing is that it is overly focused on investments and not focused enough on people (Wall Street over Main Street).  It has been successful at propping up stock prices to the point that they have returned to their 2008 levels, when they were regarded as being in a bubble.  Quantitative easing is heavily focused on investment assets.  It doesn't seem to be getting money into the hands of consumers.  Household incomes are still low.  

In short, I don't believe that the current US recession has disproved Friedman's statement.  The Federal Reserve has eschewed its traditional open market operations in favor of quantitative easing, which has affected investments without increasing the money supply available to consumers.  A better question might be why quantitative easing is widely regarded as expanding the money supply when it doesn't seem to actually do that.  

Note:  I'm sure that there is theoretical work disagreeing with Friedman's statement.  I haven't tried to cover that.  I was caught up in the questionable assertion that the US money supply has expanded without causing inflation.  I suspect that this is too new for a consensus to have arisen. This is my thoughts on one possible explanation.