To begin, it is essential to analyze both events that support the US' vision, and ones that contradict it. In World War II, the United States has sent supplies and troops to its democratic allies. Because democratic people are also considered as "free people", this would mean the United States was defending free people by lowering their chances of dying. Another example would be the Korean War. This was a proxy war (a war fought indirectly by stronger nations through weaker nations) fought during the Cold War by two bipolar superpowers: the United States and the Soviet Union. It was North Korea (communist), against South Korea (democratic). Because the South Koreans were democratic, they were considered as "free people". Similar to the situation of World War II, the United States sent supplies and troops to defend the free people, prevent complete assimilation by the North Koreans. The Vietnam War was extremely similar to the Korean War, with the United States defending the democratic people and the Soviet Union backing the communist side. On the contrary, there have been times in which America did not act as a "defender of free people".
Post-World War II, the United States agreed with France that it would assist in re-establishing France's oversea empires. This goes against their view because America is subjugating people longing for self-determination, in other words, free people. Two prime examples of the United States going against their view would be the overthrowing of Iran's and Guatemala's democratic government. Iran's democratic government was replaced by a dictator because the Iranian government wanted to nationalize the oil industries, which posed a threat (though not incredibly significant) to the United States' economy. A similar situation also occurs in Guatemala; the Guatemalan government took land from the United Fruits company, also threatening (then again, not incredibly significant either) the United States' economy. The newly established dictator by the US triggered decades of civil wars. Clearly, this is subjugating democratic people, which is also be considered free people.
In conclusion, the United States' actions in global affairs did match up to their view of themselves as a "defender of free people", but they also did not in other situations. As a result, the final answer is that their actions matched their view to a small extent. Why? It is without a doubt that the United States protected free people. Though it might not be their reason for intervening, the question is asking for the reality of their actions, not the reasons for their actions in global affairs. Though various examples and pieces of evidence have been shown to argue for both sides, there is no