The point being made here is that while the university claims they don't factor in the applicant's ability to pay the fees, they also conveniently ask for information which helps them infer your social status, making their claim somewhat more difficult to take at face value.
Bear in mind this is a thread discussing how UK universities are claiming in the face of overwhelming evidence that they are not being influenced by foreign governments. So we should be able to accept that universities are capable of lying about their internal practices.
"So we should be able to accept that universities"
We absolutely should. As of now, universities tend to get away with practices that would be called out in the private sector. Entshittification of some services plus greed plus willingness to bend your morality around someone's golden glove (which hides a fist...).
In other words, you won't be refused an offer simply because the university thinks you can't afford it.