It’s not about private v state here. If anything, it might be about selective v non-selective simply because, as pp say, it’s becomes easier to predict grades the more selective as school is.
I have a DC at two so- called “super selectives” where you could basically call the percentages of A/A every year because it will only vary by 2% or so. But the point is, the teachers aren’t over-inflating the grades. These schools watch each other like hawks anyway because a 1% rise in the As can shift them up and down the top 10 in the league tables and everyone would know instantly which schools had played by the book and which hadn’t..
Then I have another one at an independent where about 50% of the teachers are, I’m sorry to say, away with the fairies and barely know the names of the kids, let alone what level they’re at. It’s literally anyone’s guess what could happen there and there are some small classes which mean it could be all down to the predictions of these teachers who, frankly, if they were up for appraisal in the state sector wouldn’t last 5 minutes.
If an independent school gets variable results (as many do) then there’s absolutely no reason to think they will benefit from moderation any more than other non-selective schools. Independent schools vary massively across the UK and parents choose them for all kinds of reasons, not all of which are about results and often quite the opposite.