The data says this is not true. Quality of education has almost no effect on lifetime income outcomes when you control for initial test scores.
Will Dobbie & Roland Fryer (NBER)
This study uses regression-discontinuity around exam cutoffs at Brooklyn Tech, Bronx Science, and Stuyvesant. It finds increased rigor of coursework but little impact on SAT scores, college enrollment, or college graduation, which are key predictors of lifetime earnings (and typically closely linked to earnings outcomes).
https://www.nber.org/system/files/working_papers/w17286/w172...