I think the whole genius/non-genius, heavily-tutored etc conversations are just a scam to get lots of tutors in business, I really do. It plays on our insecurities as parents and encourages the more gullible amongst us to part with lots of money for teaching kids very basic skills that they should be learning at any primary school and that any normal parent could easily cover if they haven't anyway.
I think the main reason kids fail these tests is because their parents are frightened into believing that 'the' tutor is some kind of semi-magical figure who will get their kids into any school, and the more expensive they are, the better the magic will work!
The truth is that there is no secret formula and the kids are brightish, yes, but not geniuses. If your kid is on the top table, it's worth them having a go - but speed and accuracy rather than genius are the real skills being tested here, not genius level maths or anything. Slow reading but bright kids may not pass - doesn't mean they are not bright; 11+ exams do not really test for genius, and a child who is exceptionally bright in ways not tested by the exams may still fail - eg higher-level analytical skills are not really tested until A level or beyond, in most cases, but strong analytical abilities are arguably a better demonstration of intelligence than the ability to get simple maths problems correct, say. Likewise, great creative gifts will not be recognised. Dyslexic kids may fail because of the accuracy/speed factor but be way above in understanding of the topics etc etc etc.
The system for picking kids at 11 is highly fallible; if your dc passes then great, but don't assume they are a genius or are competong with geniuses on a daily basis. If they fail, they can get an excellent education in the top stream of comps and do not assume - or let them assume - that they are failures in any way. There is more than one way to achieve and 11+ only measures a very narrow range of them, and that not always perfectly, as it depends on performance in a single set of exams on a single day.