Academia - People denying the situation in the questions instead of answering
A fundamental rule of flags is: flags are NOT to be used to delete incorrect or bad answers.
That is, if there is an actual attempt to engage the question, you cannot ask the mods to delete the question just because you think it is inaccurate, gives bad advice, or challenges the assumptions in the question instead of accepting them as fact.
The correct way to express your displeasure with such a question is to downvote it.
As one of my answers was pulled out as an example, I think I should chime in here. Let me start by saying I think this is an important question and needs to be discussed. Further, to be clear, I do not feel attacked, singled out, or defensive. I think that the highlighted answer is a good example of the issue.
The issues with these types of answers is that the person writing the answer may be convinced that they are not denying the situation and think they are providing a helpful answer. The votes on answers like these are not particularly meaningful. As you say,
those answers seem to get support from part of the community because of their attitude towards the controversial issue in question
but I would also claim they get down votes because of the controversial issue in the question. Flagging the question doesn't generally work since most answerers will not see the flag. It also doesn't provide a place for discussion and puts mods/high rep users in a difficult situation. It seems to me that the comments to the answer and/or chat (and possibly meta) is the place to discuss and figure out what is going on. It might be informative to go back to my answer to see how I thought about it.
The title of the question is:
Is it ethical to apply different criteria for graduate admissions based on country of undergraduate study?
The only statement within the body of the original question (and current version) with a question mark is
Is it fair to apply different criteria to students from different countries in admissions decisions?
I think that the number of up votes on the question suggest it is an important question for our site. Despite my up vote for the question, I don't think the question is a particularly good fit for the SE format since the question "is X ethical/fair" is essentially a yes/no question and providing an evidence based answer is difficult. I think this is confirmed by the number and variety of answers as well as the up votes and down votes of the answers.
Moving on to my answer and the "charge" levied against it:
Instead of answering, some answers were suggesting that the statistics and the research they did must have been wrong and the results are not valid.
We need to first decide if I answered the question. My first sentence could (and probably should) be reworded to be
I would argue that you are using the results in an unethical and discriminatory way because you are interpreting your data incorrectly
That seems to me to be a pretty clear answering of the question. I answered "No, it is not ethical". I then tried to provide reasoning for why I answered the way I did. My answer is not particularly great in that there is little evidence to support my claim. I don't want to clarify/defend my answer here as it is too far removed from the answer itself, but I am happy to continue to clarify/defend my answer in either the comments to the answer or in chat. At the heart of my reasoning is that based on the original question, the edits to the question, the comments, and my chat discussion with the OP suggests that the classic mistake of interpreting correlation as causation is being made. I tried very hard in my answer to not claim that the statistics were wrong, but purely focused on the interpretation. In summary, I disagree with both claims about my answer (not answering the question and denying the situation).
Currently the answer has 3 down votes and three people made "negative" comments prior to the last down vote being cast. From the negative comments it is clear that my answer is confusing to people and could use an edit. The up votes (and one positive comment) suggest to me that some people see the value in my answer. Based on the mixed feedback, I would normally edit my answer to try and improve it. In this case, I feel it is better to leave it be at least for a while so that this discussion about the issue of answers that miss/deny the point can be addressed.
I think commenting and downvoting are probably the best options here. I suspect flags will be ignored for the reasons @aeismail mentions. The problem is that the "community" (defined as readers who vote) appear to have conflicting views on the matter, and what you're asking about is a form of minority protection that SE doesn't really have a mechanism for.
But I know that I read comments very carefully, and that I'd be influenced by comments pointing out that the answer is not answering the question as stated. I tend to be less likely to downvote (and I'm not sure why), and maybe that's part of the problem.