Maybe true. A relevant question is: what kind of immigration?
Not all immigrants are created equal. Australia wasn't just built by "immigrants" - it was built by European immigrants - who, apart from East Asians, have over the years built the best countries and societies. Look at majority-black cities in the US. They are.. not doing too well. Blacks in the US also make up a hugely disproportionate chunk of the violent crimes.
Different groups also (on average) hold different beliefs that can shape how the members act. For example look at how European-majority and East Asian-majority countries are different to Arab and Muslim countries when it comes to how they view women. If you're a girl in Turkey and one of your family members finds out that you simply
talked to a boy, or maybe had sex with him or that a boy got you pregnant, it occurs to the men there to
kill the girl as a punishment.
Some statistics for Turkey:
Source:
http://wikiislam.net/wiki/Honor_Related_Violence_(Turkey)
Obviously not
all Turkish men do this, but because of cultural/religious differences, it happens more often there (and in all Islamic countries) than in any European-majority or East Asian-majority country. So obviously immigrants bring these ideas and honor killings are committed by immigrants in Western countries.
The
Sydney gang rapes were also committed by men who cited their religion (Islam) as part of the explanation for why they did it.
So basically any public policy decision on immigration depends on what people you're talking about.