Why do people equate capitalism with a free market?

Knowledgeable people disagree about the definition of capitalism. Some do equate the term to "free market". Others simply define it as the economic system existing in the United States (which as you aptly state, is not a free market). The vast majority of people who have done no studies beyond listening to the pundits equate all three terms: capitalism, free markets and the U.S. system. These people are mistaken.

Since "capitalism" is a buzz word that evokes many definitions, I prefer to describe the U.S. economy as "corporatist":

"control of a state or organization by large interest groups" [1]

Words, if not backed up by careful explanation, can lead us astray. To further clarify my position (which I have gathered is in harmony - even if not idential - with yours), I will often just drop the labels and describe the forms of human interaction that I favor. I find that my position is pretty well described when I state my preference for voluntary interaction in every facet of society.

The term "Capitalism" has come to mean different things to different people. To some people the term Capitalism means what you refer to as "free market". It may be a result of the Cold War when the two spheres of power were one that supported "Communism" and another that supported "Capitalism". Given those two alternatives I will side with capitalism any day of year. Even the philosopher Ayn Rand (who wrote during the height of the Cold War) wrote about "Capitalism" as an "Unknown Ideal" and described it in a way that you would call a "free market".

I'm having a hard time following your logic, suffice to say that all of the mumbo jumbo regarding the mortgage crisis, bailouts, etc. was not caused by free markets and capitalism, it was caused by bad government monetary policy.

Capitalism is absolutely the worst system. Except for all the others.