Sounds sensible to me. I think that you are correct. Certainly it wouldn't be beneath the Guardian to report something inaccurately to support their own agenda.

Or any other newspaper.

Yes, I agree with you, the actual report seems to be all about improving the selection process so that more of the brightest students get admitted. Which is good.
Mind you, Oxford and to a slightly lesser extent Cambridge, are not quite the same as all the other Uni's. There IS an element of institutional social snobbery at Oxford/Camb, and it will never disappear completely, because those Universities exist for other purposes besides their ostensible ones.

"Oxbridge are, I would have thought, so extremely good at teaching that they should be able to succeed with slightly less excellent students than they're used to." Perhaps. But the dons with the finest minds only want to teach undergraduates with the finest minds. As admission standards decline, the dons with the finest minds will migrate to Harvard, Yale, etc.

"The only students likely to want to go to Oxbridge are the same ones likely to do well there." No. This is just plain false

In my experience, kids with no academic gifts are eager to get out of school, not to sign up for the toughest schools in the country. Seventeen-year-olds do a pretty good job of judging what they're capable of and tailoring their university applications accordingly. The ones who can't manage an Oxbridge course tend not to apply.