Immigrants to America are less likely than citizens to commit crimes. But they are still victims of crimes, statistically displacing the victimhood of native-born Americans.

This assumes victims-per-crime remains relatively constant, which seems like an extremely reasonable assumption (you've got to think it's close to 1). It also requires victim profiling towards native-born Americans isn't impacted by the presence of immigrants, which, again, seems super reasonable. The hypothetical here is, someone sees a bunch of immigrants and is less likely than before to target them in crime. Most crime is either semi-random or someone you know, so this seems safe.

So my anti-crime plan is, slowly open up immigration policy until the crime stats level out.

Absolute numbers can go up and improve things a lot for all individual participants. I recently had a conversation where someone was confused about why a mayoral candidate promised to help double the city's population – but the answer is basically the same reason you have cities in the first place. Things are better when we work together, and more people (when under a competent government) cooperate more. Everything becomes more convenient, closer, containing more niche and specific offers and jobs, allowing everyone to get something closer to what they want.

Even if that thing is a victim.