Does Mexico work the same way in K-12 education?
Public schools for kids and up to grade 9 (tercero de secundaria / middle school) are SEP´s (Secretaria de Educacion Publica) territory. Im unfamiliar with them but they are not very competitive from what I´ve heard.
Most public High Schools fall under each State University´s umbrella (although SEP has a few high schools here and there, but again, they are not very competitive from what I´ve heard) and "The State University is better than the ITESM (my state´s version of MIT) in many things, and vice versa" (Those words were said to me some time ago by someone with a high position on one of ITESM´s creations) So the State University has both a good and a bad rep, if that makes sense.