A cambio is to exchange in spanish
(Assuming the myth is referring to the United States)
The myth comes from people who don't like immigrants and who don't want immigrants to come to their country.
A person who might be xenophobic or someone who already lives in the country that the immigrants are coming from. For example an American who doesn't want someone from Latin America coming over. They may benefit from this myth to victimize themselves that the country is being "overrun by illegals".
This myth is untrue because there are many legal immigrants that arrive here legally.
