He’s entitled to publicly complain about anything he likes, just like anyone else.
The local education authority is unlikely to deviate from its processes, so it’s not like he’ll get preferential treatment for being famous or wealthy. Nor should he. But he’s entitled to appeal, as anyone is. And his child may still eventually be offered a place if they’re on the waiting list.
If his child wasn’t likely to be in the catchment for all four schools they chose, it’s likely they won’t get offered any of their choices. That’s why it’s best to put realistic options.
Maybe he’s against private education as a matter of principle, as are many other people. I believe Paul McCartney’s kids went to state schools.
School admissions policy is a tough one. I’m a great believer kids should attend their local community school, so they can walk there and their school friends live nearby in the local community. So, IMHO living in the catchment area should come first. However, it’s a pain if you move outside and then siblings have to attend different schools. But not the end of the world because the eldest can and should travel to school on their own once teenagers, unless it’s a rural area with no buses.
And giving priority to siblings can be unfair because, for oversubscribed schools, it can allow families to game the system by moving into the catchment area for a few years to get their eldest into the school, then move to a preferable (e.g. cheaper) area and take advantage of sibling priority for subsequent kids. While kids who live nearby lose out.