In my country of origin, the prestigious universities were all public and (almost) free. The most sough after degrees are difficult to get in and difficult to finish.
There, the mentality is that the only reason why would you pay for a private university is if youre not smart enough to finish the degrees on your own. I always found it intriguing that the logic is reversed in the US - the good ones are the expensive ones and the only reason you wouldnt go there is if you cant afford it. But Im glad to see that the logic in my home country does have some merit, as evidenced by the quote from your professor.