This connection is even more tenuous than your original claim that "the murder rate... lowest in countries with low immigration rates per capita". Now you're talking about crime and poverty, not murder and immigration.
Also, the first paragraph of you link explicitly says: "reliability of underlying national murder rate data may vary". I think k your argument is largely bs, and I'm not interested in researching the citations.
The second paragraph reads "Research suggests that intentional homicide demographics are affected by changes in trauma care, leading to changed lethality of violent assaults, so the intentional homicide rate may not necessarily indicate the overall level of societal violence.[6] They may also be under-reported for political reasons."
I don't think this list even makes the point that you seem to think it does, or, at least, doesn't make the point very well.