This is similar to an old canard about gay rights. "We don't oppose equal treatment for gay people," say the homophobes, "we just oppose all these special rights they're asking for."
Of course, in practice, every manner of equal treatment — from workplace discrimination protection, to housing protection, to marriage — end up classified by the homophobes as "special" rather than as equal treatment.
It's just a shell game – words bandied about for the fun of bandying. The punter can't win.
J.K. Rowling's pledge was a word game just like that. Three card monty at its most obvious.