There was once a department that was accused of sexism given the lower number of women in their residency program. Women made up the minority of that program. When an analysis was performed, they found that for a given set of credentials, women actually were more likely to be ranked highly than men. However, if women were more likely to be ranked than men, why were there fewer women in that department? Well, the answer is simple: women were simply not interested in that particular field, but for those who were, they were more likely to be ranked highly compared to men with similar backgrounds. This is why stratification is important when trying to interpret numbers, and also why statistics is part of the medical school curriculum so we can critically interpret studies. Sample size is only relevant for assessing significance in these scenarios.
Interpreting the admissions statistics here is similar in my opinion. There are fewer URMs than ORMs in medical school. However, for almost any given GPA / MCAT combination (I say 'almost' because I am too lazy to look up the entire chart), the acceptance rates for URMs are higher than ORMs. These are facts. You are right in that there are more Asians in medical school relative to the general population -- this too is a fact. Having said that, that is likely a result of Asians being more likely to apply to medical school compared to blacks and Hispanics. This would account for the discrepancy that you're mentioning here.
Ultimately, URMs are given extra leeway in the admissions process exactly for the reasons that you pointed out: low socioeconomic status, fewer community resources, educational disadvantages, etc. It's done with the understanding that a ORM with stellar stats who came from a more privileged background (college educated parents, living in a well funded school, etc), if placed in the situations that many URM applicants come from, would likely have worse statistics.
If URMs did not have an advantage, then for any given GPA / MCAT combination, the acceptance rates should be mostly similar (with variation depending on the sample size as you pointed out).