the concern amongst non-hysterical people is mass surveillance by government, not ad-hoc requests by the police for VHS tapes of people stealing packets of bacon
in this situation: the fact they're not controlled by, or accessible to the state without effort is neither pedantic or irrelevant, sorry.
After the amount of leaks and revelations in the last decade you're only embarrassing yourself if you claim that any people concerned about privacy are hysterical. Whoever is not worried is simply clueless about the power of data.
The fact that there is some extra effort required to get to the tapes does make it a bit inconvenient, but that won't do you any good if you're caught by those surveillance cameras in the wrong place at the wrong time. The investigators will almost always make that effort, since it's part of the job.
It doesn't matter who owns what as long as the government can request access to the data.