I instinctively distrust people who say they got or didn't get the job based on quotas, or if not the people themselves, I distrust the premise that appointments are made in this way, whatever the people believe.
An organisation that has EDI questions on the application form is likely to be using them correctly (ie anonymised and separate from the selection process), so will have no idea whether Applicant X is black or white, gay or straight or whatever. In many cases schools and universities attended are separate too, so that all the interviewers get to see are the applicants who have fulfilled all the 'essential' criteria and as many of the 'desirable' ones as necessary to get them on the shortlist.
After that, it comes down to the interview, at which they should all be asked the same questions. Not foolproof of course, as skin colour, accent and even school tie can come into play, but just ticking a box on a form will not get someone the job, or even an interview unless they meet the criteria as advertised.
HR can go through the applications separately to see how many people from 'different' backgrounds applied, and consider tweaking their advertising/the wording of the essential criteria etc if they find that they are only getting applications from (eg) middle aged, middle class white men in an area with a diverse population.
Also, depending on the job and the area it would be crazy to insist on a quota. In a city there is likely to be a diverse population, so an ad for someone to work in a local authority probably should attract a range of people, but in a rural village, an ad for (eg) a secretary for a local primary school is likely to draw applications from local people who want something with school hours near their homes/children's schools, which is a very different demographic. If they had to hold out for applicants of specific ethnicities/sexuality/age/sex/so-called 'gender'/abilities etc they'd never be able to appoint.
How would someone know that they had lost out because of a quota? No recruiter would tell them that, as they'd have a case for discrimination. Sometimes it might be a way of people softening the blow, for themselves or others - 'oh you didn't get it because it went to a woman' is easier than 'you weren't good enough'.