The whole reason that "left wing" and "right wing" entered into our vocabulary was to differentiate between the various flavors of Socialism (e.g. Communists on one side and Fascists on the other).
After the Fascists were defeated in World War 2, however, the phrase Left Wing remained in our lexicon to describe the Communists. Popular useage of the phrase "right wing" then began to be used by those trying to identify people opposed to Communism (in particular, Joeseph McCarthy), and was intended as an insult. Americans, being a ballsy sort of people, shrugged off the insult and generally began to equate "right wing" with Conservative, being that most Americans then and now were and are Conservative (i.e., not in favor of the great New World Order socialist Revolution favored by both Communists and Fascists).
"They say you want a Revolution, well, you know, we all want to change the world" isn't just lyrics in a song, it's also how Conservatives mock the starry-eyed socialist radical elitists. They want a Revolution, at gunpoint, to force the world to redistribute wealth and labor. Conservatives don't.
So now we're "right wing" because we oppose such socialistic folly. So be it. Just don't let anyone confuse our opposition to Socialistic Revolution with being on the same side as National Socialists (i.e. NAZIs). That's just silly, and it's just wrong.
Only if you consider the old feudal order of Europe socialist. "Right wing" and "left wing" come from the French revolution.
In some sense, what you claim may have some truth in it, but the origin that I put most faith in goes back further.
At the time of the French Revolution, the Estates General was called. The Royalist supporters sat on the Right half of the hall, and the proponants of the new ideologies sat on the Left side of the hall. Ever since that time, revolutionary ideologues have lambasted all opposition as "from the Right" and alligned with old interests, corrupt monarchy, and old power.
At that time in our nation, despite its feelings of fraternity with French in throwing off an old maonarcy, the Federalists and Adams were as leary of the Left as Jefferson and the Republican-Democrats were fond of them.