The thing is, children are by nature, bouncy and jolly and seemingly happy most of the time, particularly in groups with their friends around them. Any school that isn't actively mistreating children Dotheboys Hall-stylee is goign to be full of chattering, happy, enthusiastic kids.
So the presence of happy chatting children talking enthusiastically about their day tells you pretty much nothing other than that they're not being beaten and locked in the chokey.
I think one of the problems here, and which has also affected schools run by religious orders, is that an institution where senior staff are always appointed from within the ranks rather than from outside is going to be affected by the lack of a fresh external perspective. At best that can lead to a strong sense of identity and community, but there is also a tendency for it to result a somewhat blinkered and inward-looking ethos, which is actively hostile to outside opinions and influences.
So unless something goes really catastrophically wrong (and sometimes not even then) there is a tendency for everyone to assume that everything is fabulous just because it's working as it always has. Minor (or even major) blips are dealt with and business as usual continues.
The thing that doesn't happen in these kinds of closed management structures (whether extended family as here, or eg religious orders), and which does happen in schools with more normal management structures, is the fresh perspective that takes place when a new head is appointed from a different institution. That person will bring with them a whole different body of experience which they bring to bear on the existing structure - yes, that can sometimes be disruptive, and there will be disagreements over changes made, and sometimes there will be mistakes, but overall there will be a realigning of the school's ethos and direction in ways that open it up and renew it.
I suspect that what has happened here is exactly that entrenchment of perspective and narrowing of vision arising from the fact that the entire SMT of this school is taken from a dynastic extended family with a very strong original vision, but one which has not been strengthened and modified by being systematically challenged and refreshed by any outside influence. And yes, having seen at first hand some very similar issues within a school run by a religious order, I would be inclined to take the Ofsted criticisms seriously, and to take even more seriously the SMT's knee-jerk reaction that nothing can possibly be wrong because they're doing what they've always done and therefore it's fabulous.
The fact that things are jogging along perfectly nicely and individual children are happy and getting into good senior schools does not at all mean that there are no problems, or that things could not be significantly better. In fact, is this not exactly OFsted's criticism of 'coasting' state schools in 'leafy' areas, ie that they get good results, but actually given the advantaged nature of the intake, they could and should be doing a great deal better? I would also be very concerned by the finding that a high proportion of teachers feel that their professional development is not being well-supported. Essentially that means the people delivering the hands-on education think they are not being helped to do the best job they possibly could - and for the managers to respond by saying, 'nonsense, everything's fine here' is even more worrying.
All schools should be constantly questioning their own practice on all sorts of levels, and the arrogant and complacent reaction of the SMT here sets major alarm bells ringing.