Like I said, the causal part (as others pointed out) hasn't been investigated thoroughly. We do know that street criminals have victim selection metrics that are reported to be based on gate, gaze and attentiveness. The idea being a victim who is easy to take relatively unaware and will comply.
As far as I know prediction of having a gun doesn't enter into it or has not been tested.
We do know that burglar interviews and time patterns of such suggest they try to avoid running into an armed homeowner. Our patterns differ from countries that don't have significant numbers of home guns.
You have to get down to a more microlevel for causal interpretations. I remember Lott saying that gun locks were related to more rapes, implying a causal link. That was just global rates and no attempt to look at rape dynamics. It was unfortunately a silly causal stretch.
The point that we haven't seen a global increase in crimes and the crime rate of CCW/CHL types does speak to the CHL population itself not being a major risk of increasing gun crime.