I think you're right, OP. I think often these kids have a father who is a high earner and a SAHM who ferries them back and forth, or both parents work and they have a nanny. They also often have a tutor on top of private school. Privilege upon privilege....
Back in the real world...
All my friends work, some in Tesco, some in offices, a few for the local council. Our children (now in their 20s) did an activity, mine played cricket, some did martial arts etc. none of us used tutors and our children went to local primary and secondary schools (no grammars here).
Almost all our children have gone to uni. 3 to Oxford, 1 to Texas on a full scholarship, the others to Durham, Loughborough & Manchester amongst others. One graduated with a first even though he was never expected to independent (autism) and spent most of his early years running away from school.
My boys are the first in our family to go to uni. We are not high achievers, more senior/middle management 'plodders'. DS2 who didn't do great at school just graduated with a 1st and an award for being the highest achieving student in the country last year, he's now off to do his masters. DS1 who was always in the top sets and has a good degree just plods along without any thought of what he could achieve should he put his mind to it.
We didn't have tons of money, nor a luxurious lifestyle but what we all had was an interest in our children and invested our time in them.
That's all you can do. They have to want to succeed and put the work in to do so. You have to invest your time in them. There are so many variables on how a child achieves it's impossible to make a statement like the one you have above. you can't write a child off because they don't do extra activities, or don't go skiing in the Easter break.