Yes, this is more or less my claim, and no, I have no data to back this up (other than the general fact that Hmong representation is so low…) If you want to live in a fantasy world that the Pedant just creates his own reality, feel free to do so. Or take the time to evaluate the broad patterns that result, which cannot be hidden behind exceptions and behind-the-curtain processes.
Perhaps this complaint, and others, will begin to tease out the sort of data you demand. I rather doubt it; Harvard lawyers were not born yesterday nor given a marginal education. 
You are exactly correct about the challenges all of the underperforming groups face in terms of overall SES background and the other factors you mention. We’ve been through why that is elsewhere, and why some groups succeed while others always seem to occupy the same position on the SES tier.
As I said earlier, they why does not matter for the sake of this discussion.
But what happens for a Hmong student is that the box they have to check is “asian,” and therefore the peer group with which they compete is “asian.” The talent level–academic and “other”–required to be accepted as an asian is its own category. Because the general, overall defacto quota is by broad race groups (the ones listed out here, Hmongs compete with asians; not with blacks or whites, on average.
A stellar black student from a low SES background will get evaluated against other black applicants. A stellar Hmong student from a low SES background will get evaluated against other asian applicants, where the bar for the group is much higher.
The institution is only going to get credit for the OMB groups should they be audited, so to speak (formally or informally).
You are right that an applicant within a given group who has high standout skills not typically associated with that group also has a leg up. Any mechanism to stand out in this highly competitive process is a leg up. Black football athlete? Very common; need scores. Black SAT scores of 2250? Come on down! Asian perfect SAT? Very common; need “other.” Asian basketball star? Come on down! Asian high-scoring; violinist? Hmm…we’ve already admitted quite a few of those…etc etc etc
This is how the admissions process works, DSeid. Each application is considered seriously; when it comes to actually offering admission, a defacto race quota is maintained so that the class does not become cosmetically lopsided by race.
What this ends up meaning is that each applicant is compared with their race peer group.
And that is the asian complaint. Asians are compared only with other asians, and the asian standard is much much higher. Therefore this is a bias against asians.
I do not pretend this is absolute for every individual. Of course a school might recognize the special struggles for an asian who is Hmong, and make an exception. But if you stand back and look at the overall pattern, it is abundantly clear what happens, and why. We need a cosmetically diverse student/workplace body. We are not trying to “correct” past injustices per se; we are trying to smooth out differences that would otherwise become socially untenable were we not considerate of race alone. If you are black, we are not going to hold your wealth and opportunity against you if you are a great applicant, because we need more blacks. If you are Hmong, it may not help you much to have a low SES background because we have plenty of asians.