In the UK, I think both play a part. Like it would say a lot of someone went to a rubbish school but still got into a really good uni. Or if someone went to private school, the kind of people they probably associated with. It’s not definitive by any means but experiences colour a life.
My brother m’A passed the entrance exams for a long list of private and selective schools and received number of scholarships. My father decided to send him to a selective rather than a private school (even tho his tuition would have been paid) as he wanted him to be with other children who also had to work hard for their place. He chose education over status (coz trust me, we know people who went to those schools and don’t they like you to know it).