YY, maria, but to be honest, that is true of so very many people!
I agree with eccles that the metrics are crude.
I went to Cambridge having felt comfortably middle-class all my life, having gone to a private secondary school, having two parents with PhDs, and having had my privilege drummed into me. And I still encountered people who treated me as if I were disadvantaged.
One does.
The reason being that, sadly, in this world there are always people who do not realise that their enormous level of privilege is anything but their due.
Likewise, my partner - who is the first in her family to go to university, who went to a school with very little history of sending students to university, who grew up with very little money, etc. etc. - is also, persistently, shocked and hurt when people do not assume she is middle class.
The problem isn't primarily how people feel and what they want to identify as, IMO. You can't do much about that. What you can do is to see if there's a way to give students who had a rough time another chance. It may not work perfectly, but it is better than nothing.