I've not heard that but apart from primary schools, there is only one Catholic comprehensive anywhere near me and it's not on the doorstep - easy to reach by one bus though. There's also a Sixth Form College a bit nearer, again on bus routes from Bromley.
They are both highly regarded and their intake is from a cross section of society. I've known people who went to one or both and a couple of teenagers now who are currently at the comp, a colleague also has a child there, her oldest one left a couple of years back. They've all said how good the school and the Vlth form are and what happy atmospheres they have.
I think if some of the schools surveyed are selective grammar schools or private schools (I'll go back and check your link because they may have said), they will be picky, they always have been and has nowt to do with religion.
We have selective state grammar schools near us (not religious tho' one boys' school was founded as a CofE school & at certain times (founders day, that sort of thing), some of the old traditions are brought out but in every day teaching there was no proselytisation. They take children from all religious traditions and none. My sister, cousin and I went to one, my children and niece did too, and it was fine for us but definitely they can be choosey.
The highly academic independent schools are also extremely selective; my husband and one nephew went to one not far from us (again a bus ride), which was originally a Christian foundation, they'd agree with my assessment but they loved their school.