I personally do think that immigrants are more likely to commit crime. But like the stats you get on black people committing more murders - I don't think this is something inherent to black people or immigrants.
Black people tend to live and concentrate in urban areas, and the crime that tends to happen in urban areas are these kind of crimes. It makes sense that they will be over-represented in those crimes because that's where they live. I would guess that almost all poaching or wildlife crimes are perpetrated by white people. This isn't because white people love to steal falcon eggs or misuse agricultural diesel - it's because these crimes happen in rural areas and white people live in rural areas.
Same with immigrants - the profile of an immigrant is most likely to be a young man. Most crimes are commited by young men. More crimes will be committed by immigrants because of that - it's just stats.