Not everyone thinks this, but I know an extreme right-winger who thinks this. He is also a conspiracy theorist who thinks non-white people are out to get white people so, yeah, odd.
Not every immigrant is illegal or bad. I know a girl who didn’t speak English for 3 years when her family legally immigrated, so of course she’s been told this.
Reality is a team sport, to some people. You’re not going to catch them out with logic. They don’t give a shit about consistency. It’s simply not a factor in how they decide what’s true.