I just think that's its a flawed logic to attribute the paying of more money to a private school as corresponding with a 'greater' drive to succeed in VCE. That's a fallacy imo - hence the use of the gross stereotype to exaggerate it.
I agree with this to some extent, while you aren't paying for a greater 'drive', what you are paying for is a better learning culture. Most of the big wealthy private schools (Scotch, Grammar, PLC, MLC etc) carry a culture where the students want to do well, where even the 'jocks' make an effort, especially during VCE. Students at private schools don't really think about how they have to do well since their parents are paying alot, rather, since their parents are more likely to place a focus on education, these students are raised in an environment where they are encouraged to do well.
You can see this reflected in other non academic areas such as sport - why do so many of the elite AFL players come from private schools? It's because the parents / staff / other students encourage a culture of performing at your best.
I don't think socio-economic status DIRECTLY affects how well a school performs, especially since the stereotype of everyone at private schools being extremely wealthy is an exaggerated falsehood. What allows the top private (and public) schools to succeed year after year is a continuous belief throughout the school that doing well and working hard is something to strive for.