This is anecdotal but most of my closest friends got their DPhils at Oxford and all of those who wanted to pursue academia got postdoc positions at 'top schools

This is anecdotal but most of my closest friends got their DPhils at Oxford and all of those who wanted to pursue academia got postdoc positions at 'top schools' based entirely on quick chats and someone in the lab who knew the group they'd been with at Oxford vouching for them. I've heard people say they've been told the main differential between them and other candidates was the school they went to, not the academic output they had during their PhD. So this isn't too say you're wrong - there is definitely something about better students go to better schools and there should be some correlation there, but this is way bigger than that.