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.
Unfortunately I’m familiar with the term. It refers to Latin people immigrating into the U.S. without documentation by swimming across the Rio Grande river which forms part of the border between the U.S. and Mexico.