Really? I can't click on any link on the web about Independence Day without being bombarded with messages about freedom and liberty which leads me to believe that it is in the minds of US citizens when this day comes about
"Freedom" and "liberty" seem to be more like buzzwords used on the 4th of July than they are concepts pondered and/or specifically celebrated by the citizenry at large. (But perhaps that's just my biased/warped perception.)