You are reading correctly, this has always been the case. It is known as AVR (Automatic Visa Revalidation).
However, it doe not apply to nationals having left US for their home country, thus Mexicans cannot re-enter US under AVR from Mexico. Essentially, Mexicans need to get new visa anytime it expires, unless they are visiting and re-entering US from Canada or the Caribean.
And Indian or Chinese national, in this situation, could re-enter under AVR after visiting Mexico, but not a Mexican.
That is proabaly why you've never hreard of it: it rarely applies to Mexicans.