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
Words like freedom and liberty are part of the standard rhetoric around the holiday, yes, but few are consciously thinking about those ideas. Practically speaking, the words are on the same level of symbolic pageantry as the fireworks, hotdogs and beer. But I don't think that disconnect is special to fourth of July or to Americans -- in my experience most holidays as well as religious ceremonies are similarly disconnected from their meaningful origins.
Yes, there are plenty of messages about "freedom" and "liberty", but that doesn't mean the concepts are truly in the minds of the posters.
"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.)