I think that most people actually believe this at their core, but they've been told so frequently that there should be limitation on their freedom that they have a tough time rationalizing what that actually means. Propaganda is extremely powerful and even the most intelligent people are susceptible to it.
I'm not so sure people actually believe this at their core. I think their beliefs are informed by what they are told. As you say, propaganda is extremely powerful.
When I talk to folks (irl) about this stuff, I'm reminded of a (hypothetical) child who is told that she is stupid, ugly, and worthless throughout her life. In later years, she comes to believe she is stupid, ugly, and worthless. Same with voters. They believe that which they are told over and over. Like children.
It is what informs their perspective about rights (their own and those of their neighbors), laws, and the state's authority over their lives. Heck, people still think Lincoln was a wonderful president, that the war on the south was about freeing slaves, and that FDR pulled us from the depths of depression. Again, propaganda is extremely powerful.
So, when I see folks raging against the machine (in this case, regarding the "right" to film cops), I wonder what informs that perspective. Is it an understanding of natural rights versus legal rights? Or, is it merely emotion-driven blowback stemming from an affront to their personal (and inconsistent) notion of their rights? As I mentioned, once someone agrees that their rights are granted by charter, they essentially acquiesce that anything the state says goes. That is, until they "vote the bastards out," at which point voters replace them with a new set of bastards.
Here, I'll leave a relevant quote taken from
this piece (which, by the way, is a good read that has very little to do with this discussion):
Power concedes nothing without a demand. It never did and it never will. Find out just what any people will quietly submit to and you have found out the exact measure of injustice and wrong which will be imposed upon them, and these will continue till they are resisted with either words or blows, or with both. The limits of tyrants are prescribed by the endurance of those whom they oppress. - Frederick Douglass
Sadly, the endurance of the oppressed - at least, in the U.S. - seems limitless.