You may be right, but the post may well still be in 'unanswered questions' if I hadn't picked it up and I am the only one keeping it going! There isn't much to say other than 'yes, what a scandal' because I would assume that HEers are already putting people right on it and from what you are saying putting pressure on LEAs to put the record straight.
We appear to be guessing at what LEAs want, since I don't work for one and don't know anyone who does I can't say what their policy is except that they were lamenting about the falling birth rate a few years ago so they are probably pleased to have a bulge.
I do know it all comes down to money. I haven't spent much time researching it but in 2009/2010 average funding for a primary school pupil in England was £1100 per term and it can only have gone up. Secondary pupils is always more. Therefore if a family with 3 children in a primary school decide to withdraw them and HE the school loses nearly £10000 a year and yet they still need the same number of teachers, TAs and resources. Of course they don't want to lose them! Schools struggle for cash they want classes full. Schools do a really hard sell, they want to be chosen, they do not want to lose pupils to other schools, the private sector or HE. They stress the reasons why parents should chose them, they don't go around telling them they would be better off elsewhere. (this is why Heads are not keen on flexi pupils, they don't want resources taken up without the full £3,300)
My guess is that if LEAs start treating it like a very viable choice and telling every potential parent 'have you thought about doing it yourselves?' they will want more control. I am not saying that it is right or wrong, just that it is highly likely. That will be a more important battle than people saying 'is it legal' when they are not much bothered, have never thought of doing it and have no intention of ever doing it.