> It's also possible that the scientists correctly infer that, even conditional on having the same resume, female applicants were overall of a lower quality.

Somehow you missed the point that, in the experiment, only the names were changed -- the resumes were identical, the applicants were identical, the level of experience and education were identical. Only the names were changed. The reviewers therefore judged the applicants only on the basis of gender. That's both wrong and illegal.

> The study doesn't prove whether this disadvantage comes from people discriminating against women merely because they are women ...

That is exactly what the study proves. Exactly. As in all good science, only one element was changed -- the name of the applicant. The reviewers changed their evaluation based solely on the applicant's gender, nothing else.