He's correct on a factual level:
https://www.brennancenter.org/blog/americas-faulty-perceptio...
There's a wider context, though, where violent crime during 1940-1960 was abnormally low compared to the earlier part of the century (which had violent crime rates similar to today), and then it shot up in the 1970s. And the 1900s in general has been quite low to historical homicide rates in colonial times.
http://sites.nationalacademies.org/cs/groups/dbassesite/docu...
All of this fits my point that you can't really draw conclusions one way or another from the crime rate.