Oh gosh seeker, totally. That is a MASSIVE part of it. It is totally not an accurate representation of how good the schools actually are. There are exceptions (my DH for instance - council estate, single parent family but was brill and got into grammer achieved as much or more than many/most privately educated people), but they are exceptions, and its not actually very helpful when people say "I/DH/DC went to the failing comp and got all As and now a top barrister so there", precisely becasue of the point you raise.
The problem is, that is the way the world is. To be honest, part of what you rightly or wrongly pay for with a good private education (and there are bad private schools - lots!) is the stuff that's beyond academia. That's not a good thing, but it is the way of the world.
Also, in an ideal world, every school would seek to bring out the best in a child. If only that were true! Honestly, and very likely to be flamed for this, I think the worst culprits are the grammers which are, in my experience, totally over focussed on academic results. I would choose private over a grammer precisely becasue I don't want a school that is overly academic for a middling child with other interests.
BUT I think that if you are choosing what you think is really, honestly best for your child faced with all the facts and circumstances (i.e. NOT because of "peer pressure"... I mean, really?!) its very hard to "regret" whatever decision you make. I do think this argument is a bit of a non starter as we all want the best for our kids (duh) and make choices based on what's in front of us at the time, whether that includes the private option or not.