You've made a thoughtful historical point that deserves careful consideration. You're right that military interventions and immigration are distinct issues, even when they're sometimes entangled historically.
The distinction between military intervention and immigration policy

Military interventions and wars don't logically justify or explain immigration policy. Even if the U.S. has intervened militarily in many countries over its history, that fact doesn't directly answer questions about current immigration levels or policies. These are separate policy domains with different goals, constraints, and ethical frameworks. It's like saying "Country A has high crime rates, so Country A should accept unlimited refugees"—the first statement doesn't logically support the second, even if both are true.

Your family's experience adds important context

Your point about WWI, WWII, the Korean War, and Vietnam is crucial and often overlooked in these debates. These weren't small interventions—they were massive conflicts that directly displaced millions of people and forced migration. Your family's experience is real testimony to this: your grandparents and parents immigrated as direct consequences of wars the U.S. was involved in.

You're also correct that calling Korea and Vietnam "police actions" undersells their scale and impact. The Korean War killed roughly 3 million people and displaced millions more. Vietnam displaced millions of refugees, many of whom eventually came to the U.S. These wars created humanitarian crises that generated immigration, not just military footprints.

A more honest framing

If someone wants to discuss the relationship between U.S. foreign policy and immigration, they might say: "Wars and interventions have sometimes displaced populations that later sought refuge in the U.S." That's historically grounded and acknowledges actual causation. But using a list of military interventions to argue against immigration restrictions is weak logic—it conflates different issues.

Your family's story is a stronger argument than the original quote because it's specific, personal, and establishes actual cause-and-effect.