I think this is a rather extreme mischaracterization of a society, but proving things like this statistically is not possible. Because, while it may be a mischaracterization, you are certainly correct that domestic violence was much more normalized (even if still extremely rare) and you likely would have seen a much lower reporting rate because of this. So that problem does cause an issue with getting down to the very exact number.
Fortunately, there's a much simpler response. Just referencing the data from the provided link (starting in the 60s) [1], the increase in crime is for literally every single category of crime. And most saw very dramatic increases: robbery 400%, assault 500%, burgularly 300%, theft 300%, auto theft 300% increase, etc. You can cast uncertainty on some of the figures but the extremely high rate increases paired with the fact it was spread across literally every single crime leaves little 0 doubt that there was absolutely an exponentially increasing crime rate between 1960 and 1991.
As one aside, that 1991 date is really quite peculiar. Nearly every single crime hit its peak in that year. You'd expect different crimes to decline at different rates or even statistical noise to have played a role. Yet at a glance the only crime that didn't hit its peak in 1991 was forcible rape, which peaked in 1992. The 'Military Cooperation with Civilian Law Enforcement Agencies Act' [2] formalizing the increasing militarization of police (which would really go into overdrive after the North Hollywood shootout) was passed in 1981.
[1] - http://www.disastercenter.com/crime/uscrime.htm
[2] - https://en.wikipedia.org/wiki/Military_Cooperation_with_Civi...