Inquiry - how having this data proves that they do such a thing? Maybe none of the black applicants had necessary qualifications?

To answer your question - if there is such a complaint made, I'd appoint another qualified hiring manager(or HR person) to sit in on any future interviews with this person and give me their report on the situation.

How could such a complaint be made?

....the same way any other complaint is made? If you think you have been discriminated against when interviewing you'd complain to your local department of labour or equivalent, they would then bring it up with the company and it would have to be investigated.

Why should we trust your HR person who is allowing this happen?

Allowing what to happen? I don't really understand your question.