Source? Pinker’s The Better Angels of Our Nature had lots of issues. But its core observation that one’s homicide hazard rate has almost monotonically fallen across human history would imply that small, ancient group were way more violent than our modern societies are.
This is relevant because the metric we're measuring now is exactly that: crime, not violence. WWIII could break out tomorrow, billions could die, and crime could still go down.
Lots of the deaths appear to be separate from war [1]. We have lots of evidence of violent crime in non-state socieities [2].
Where you might have a point is in the reduction of anonymous property crime. But that's just because small societies don't tend to have privacy. The property crime may still happen, it will just be resolved comunally or bilaterally using violence.
[1] https://historyandarchaeologyonline.com/bog-people-criminals...
[2] https://www.researchgate.net/publication/279610323_Violence_...
So for instance a big one is interpersonal 'justifiable' crime, versus random crime. There are places where if you insult somebody's integrity, they will kill you. Add some alcohol into the mix and these sort of places can have some rather high homicide/assault/etc rates. But on the other hand in these very same places, your chances of falling victim to random crime is basically zero, so they feel extremely safe in spite of having many crime rates comparable to places that feel extremely unsafe.
And data about the nature of crime in the past is strongly suggestive that it also had a similar character. People would not hesitate to use violence in the case of interpersonal conflicts, but the chances of falling victim to random crime was likely significantly lower than it is today. And I think these are the sort of crimes that people mostly care about, and it being a result of social alienation does seem like a perfectly valid hypothesis, though I'm not sure if in present times South America and others would falsify it. From an outsider's perspective, they seem quite socially cohesive, yet have exceptionally high rates of criminality.
Where are you thinking of? What I've seen, more commonly, is societies with lots of crime having ways for the wealthy to insulate themselves for it and then, acting against a background that has normalised high crime, feeling very safe. Versus societies where everyone is more mixed together where folks are constantly paranoid about vanishingly-infrequent crimes.