I nearly posted about this yesterday and decided against because I thought it might cause a row! But there's an interesting wrinkle in the Oxford admissions process (I have no idea whether Cambridge is the same) that does actually incentivise this, and I think my older DS inadvertently benefited from it. And in summary yes, if you were the kind of parent for whom Oxford entry was the only thing that mattered (which would be weird) you might well be better off deliberately sending a clever child to a bad school. (This isn't so much about state versus private, as high achieving versus low achieving schools - which isn't the same thing given that some state schools achieve brilliantly and some private schools achieve poorly.)
Because Oxford score your GCSE results against the average achieved by other pupils in YOUR school in YOUR year, clever kids (especially those with home support, educated parents, books everywhere etc) taking GCSEs in badly performing schools do have a significant potential advantage over kids with exactly the same potential and exactly the same social background taking GCSEs in high-achieving schools. So you could have two kids with the 'same' level of cleverness/potential attainment [however you would define that], but if Kid 1 is at a school that achieves very poorly at GCSE and Kid 2 is at a school that performs very well at GCSE and they get the same GCSE results - or even if Kid 2 gets markedly better GCSE results - it's basically impossible for Kid 2 to score as highly on this measure as Kid 1.
DS1's school was epically shit - I think the average GCSE grade is a 4 - so his handful of 8s and 9s made him look like a flipping genius (which he isn't, although perfectly good enough to be at Oxford and doing well there now). In a year of 150 pupils he was the only one to get a 9 in any subject and he knows one other person who got an 8.
Kids who have family support and other social advantages and who are good enough to be at Oxford or Cambridge (or imperial or LSE or warwick or Manchester etc etc) will do well at GCSE with the minimum of handholding. I don't want to be insensitive but the truth is GCSEs should be easy for these kids (NB not talking about kids from difficult backgrounds/young carers/SEN etc), and they should be able to get grades in the 6-9 range whatever school they're in.
So yes - although I would never have done it deliberately - sending a genuinely academically clever child to a low-achieving school is actually a tactic that might materially benefit an Oxford application. Whether it's healthy or sane to pursue this course of action is another thing altogether of course.
Although I was delighted DS1 got in to Oxford and I do think he's there on merit, this bit of Oxford's admissions scoring obviously doesn't account for families like ours (middle class, university educated, full of privilege but politically stubborn enough to send kids to the local school even if it's a bit crap). But maybe there aren't enough of us to be statistically significant - most families like ours around this area go private.
(Disclaimer: obviously the GCSE score is only one of several elements in Oxford admissions decisions)