It isn’t clear in the article, but the local authority it refers to could well be Bromley, where I grew up and attended the Grammar.
Either way, it certainly reflects my experience, where it did indeed appear fairly random who got selected and who didn’t. What’s more, plenty of people I went to school with had extra private tutoring to get them through the 11-plus (I didn’t), which was why it was disproportionately posh.
Resources will always be limited, and I don’t oppose choice in principle, so I’m not opposed to randomness in allocating people places. But just as catchment areas give rich people who can afford to move an advantage, selection rewards those who can afford extra support. If we’re going to have randomness, the least unfair way of managing it would be an actual lottery. Misty eyed nostalgia about the wonders of Grammars doesn’t get us anywhere.