A radical statement indeed. In fact, it's the one statement no sane person is willing to make right now, but I might put it forward. Let me start by saying that this is an economic argument more than a technical analysis argument. Ultimately, the price action of the market will give you the best answer to this question, so take it with a grain of salt.
First, when people say "don't fight the Fed", they are assuming some sort of invincibility, as though they can inflate at will. But wait a second, haven't housing prices plummeted over the past few years? Where's the inflation there? The reality is that the Fed has control over certain things, like interest rates, liquidity, etc, but the choice to spend money is ultimately the choice of the people with money in the bank (you and me). The Fed cannot force us to spend money. They cannot make you buy a house or a car. That's why you hear the phrase "pushing on a string" to describe a liquidity trap the Fed may be finding itself in right now. They can pump out all the money they want, but when there is no consumer demand and saving is on the rise, then they are helpless to inflate.
Second, in terms of the market, "Fade the Fed" is a sound investment strategy since 2000. Every bubble they blow eventually gets blown to bits, so shorting a Fed-generated bounce has been a winning strategy for nearly a decade. On the other hand, buying a Fed generated market bubble has ALWAYS been a losing strategy.
Should it be "Don't Fight the Fed", or "Fade the Fed"? The choice is yours.