I don't like her at all, and I think the way she runs her school is insane. I am very much unconvinced by their model of science teaching, and think their students will come unstuck at A-level/uni.
BUT
I do think she has a point about luck.
If you've got a secondary age child, do you know if they're being taught by a permanent teacher (not long term supply) in all their subjects? Do you know if that teacher is a subject specialist? Do you know if they're qualified?
If you've got a primary age child, do you know how much of their week they spend in the classroom being led by a TA?
It is, in some cases, luck as to the quality of teaching your child will get. And it is true at secondary there will be a number of children where their parents are helping them at home or paying for a tutor.
BUT I also agree with those on the thread who say that parents don't have the skillset to do this. For sciences, at GCSE, you could teach your child factually correct science to the required level, and they'd lose out on marks because of the way the markscheme works, in places- for example. AQA (the exam board I'm most familiar with) are extremely specific about the language used in some places, and if you're not also familiar with that, students can lose a lot of marks (no, I don't think this is ideal, either).
And, to be honest, many parents wouldn't have the subject knowledge either. Or if they have it in science, they don't have it in English (me) or music (also me) or art (also me) etc.
What we need is for all schools to be able to ensure students get a certain standard (not necessarily style) of teaching, from a qualified, consistent subject specialist AND for schools to have funding to provide intervention for those falling behind. Smaller class sizes would also help.