I think you hit a lot of hit on the head. This does have a lot to do with application selection. I've read publications written by some admissions directors that touch on this very issue, which is a real issue. On top of that, URM candidates are the most likely (not to be confused with a majority of them) to return to places such as those they came from to work. These are both major parts in selection criteria of URM candidates and are both needed, especially in certain regions of this country.
I agree that there is no such thing as an automatic acceptance, for anyone. To be fair though, I don't think anyone here can deny there is a quantitative discrepancy in admissions standards between certain racial and ethnic groups. It is these discrepancies that are seen and to some groups raise the question of 'why do I have to be better and reach a higher level of excellence than someone else just to have the same opportunity?'. I think this is a very fair question as well, in fact, it is the same question that many disenfranchised groups have asked for centuries, not just in this country, but all over the world in probably every time period imaginable. So to discount one group of people for questioning the validity and merit of an institutional bias, real or imagined, with BS phrases like 'check your privilege' in my opinion are pathetic. I think that a lot of people view things like this through the lens of hypocrisy. On one hand, you will see certain groups of people shouting that they are being discriminated against, and then this same group happily accepts policies that might favor them over another. I'm sure most reasonable people can understand that there exists a disconnect here.
I also think it is interesting that both of these issues are the same for different groups. For example, feeling the need to point out the obviousness of benefits that are accrued to white people is a little bit of a spit in the face to white people. I don't think it is hard to see why people won't take to this well as it is really a belittling of anything they have accomplished in their life. It is literally the exact same problem that URM's face when people assume that the only reason they made it into a place like medical school was because of admissions bias. It is unfathomable to me how one can protest the thoughts of one, but actively promote the other. Its a bit more hypocrisy than I can swallow, whoever it comes from. One thing that is consistent among all groups of people is that, in general, we tend to feel more comfortable around people who look, think, and act like us. Nobody is immune from this. Were the country to be composed of 70% chinese people, there would be bias towards ethnic chinese and on and on and on. So for a URM to literally go out of his/her way to remind someone who is white that he/she has privilege is just childish, belittling, and likely comes from someone who as at best a little bit prejudice, and at worst, at racist.