I have personally gone through HR trainings that directly contradict what you're saying. "just and fair" allocation is also a vacuous qualifier. According to whom? If it's just and fair allocation according to someone that believes in equality of outcome, then you're not disagreeing with the comment you're responding to.

I think in practice, equity does in fact mean equity of outcome. Pretending that that's not the case feels like gaslighting to people, and drives people away from DEI initiatives.