This is a terrible argument. The reason those populations were so low is Mexico and the Southwest were mostly pre industrial until the 50s, and had the demographic numbers of pre industrial societies. Meanwhile Anglos were industrial and could outnumber.
It can be difficult to grasp just how recent the Mexicanization of America is. In the 1970s, less than 70,000 net Mexicans were immigrating per year. Then from 1980-2010, you had about 700,000 net migrating every year, on top of Baby Boom levels of TFR.