So obviously I welcome any anecdotes to the contrary, but I was always told that in my formely communist country(Poland) university admissions were extremely fair. Everyone had equal chance if they passed exams well enough - in fact messing around with this system was guaranteed to get you in prison for corruption. And in there were many examples of poor families from very disadvantaged backgrounds sending kids to top universities because they studied hard enough to pass the entrance exams - there was no bribe you could give anyone to get you in, because the principles of fair admissions were upheld as the greatest value. I'm sure there are examples of it happening that we could find, but my understanding is that it was incredibly rare.
Now, top posts at universities - that's a different situation. To be the dean you had to be in the party and know the right people to be considered for the position. But students? Anyone could get anywhere and study completely for free.