We reanalyse data used by Le and Miller (2005), where it is found that students from low socioeconomic status (SES) backgrounds have lower university participation rates than those from higher SES backgrounds. We utilise the concept of eligibility to attend university - here defined by both possession of a valid ENTER score and the value of that score. We find participation among those with similar eligibility to attend university does not vary by SES. Conditional on their ENTER scores, students from poor family backgrounds are as likely to attend university as those from better-resourced families. Hence, we see little scope for equity-based tuition scholarships to rectify differences in participation between these groups. Instead, we find that possession and the quality of ENTER scores (eligibility) does rise with SES. Further analysis and policy targeting of the linkage between SES and ENTER scores is more likely to produce superior equity and access outcomes in higher education.