Phew! So much confusion here!
The problem isn't so much the cliche of 'he's one of us, give him a job' (equally this could be said at the working class level). The problem is the poor thinking that ends up with a result that looks like a 'he's one of us' bias.
This is the narrative that says 'top public schools both recruit and produce the elite' - if that is the case why pay? (since if they recruit the elite and the outcome is.. the elite, what value are they adding (or put another way, real education worth paying for would recruit the dull and produce the elite))
At Uni, there is a similar narrative - top unis both recruit the best and produce the best - again, why pay, since you have the best already, what value is the uni adding, again, surely the better university is the one that takes the lower abilities and makes more of them.
Employers are duped by both. They believe that if they recruit from top universities, they are getting both pupils selected by ability AND pupils who have been through the best universities.
In fact what employers do when they recruit from top universities is recruit from public schools, with outcomes predicted by primary-school level performance. They do not employ people with innate abilities higher than the average, in fact they recruit people with similar abilities to the normal population with the only distinguishing feature is resources spent on education.
What we, as a country, need is the high achievers from any walk of life to be given the best resources for study HOWEVER what wealthy family would, in truth, be keen to see their offspring move down socially because they have middle-ranking intelligence, because a better able pupil is available to the education system?
This is why the UK did so well in wartime and in crisis. In crisis, johnny toff who is thick can be cast aside for bobby working class if bobby is going to be better for the country's mission as a whole in johnny toff's job.
In fact top public schools do NOT recruit the elite - they by far in the majority recruit on ability to pay.
The output is therefore a function of money. The public school system demonstrates that mediocre students with a great deal of money spent on their education do well and therefore that anyone with a great deal of money spent on them will do relatively well, irrespective of ability. which means class/money rears its head but also the attendant outcome, that many people in jobs recruited through private school and top university aren't the best able overall.
People with little money but high ability will do averagely with few resources, but much better than the average with maximum resources. This is backed up by data that shows a middle grade pupil from a comp is more likely to get a first than a high grading student from public school.
if employers want to recruit the most able, therefore, they should recruit middle to high ranking students from comprehensives into their top level recruitment programmes, and this means they should target high performers from middle to low-ranking universitiies ahead of mediocre performers from top universities.. but guess what, britains top 100 employers only go to 10 universities in good times, and 5 or less in 'bad' times, thus ensuring a public school bias straight away, and a higher probablity of recruiting a mediocre student in terms of ability.