the actual rate of sex crimes has been more or less unchanged in Sweden between 2005 and 2014, despite the fact that immigration has increased during the same time period.
True, but while the rate of sex crimes hasn't changed despite the rise in immigration, the rise in Muslim immigrants may effect who carries out those sex crimes. The rate doesn't have to change, but the demographics of the people who commit those sex crimes can.
So, are you saying that imported rapists are pushing out native rapists?
Something like that, yes.