So treating instability in these countries as mainly the result of U.S. involvement seems overly simplistic. Many U.S. interventions have contributed to instability, but many forms of U.S. involvement have also contributed to stability. Not to mention the enormous amounts of economic resources that come from the U.S. and enrich other countries through trade, investment, and remittances.
You can make a humanitarian case for immigration without reducing the causal history to "the U.S. destabilized these countries, so the U.S. owes them entry". The history is much messier than that.
Countries do prevent other countries from using their airspace, by the way.
As for U.S. territory, yes, you can make a case that it's the collective property of American citizens who then decide how the property will be governed through their elected representatives. How is that anti-liberty?
On top of this, do you think legal migrants are equal to your fellow country men?
Why else the need for this non sequitur?