I don't know the reasons behind AMCAS' method of identifying nationalities or residency status of applicants, but I think it is there to make it easy for them to get a clean data for analysis.
In my personal opinion, there is no difference between a permanent resident vs. a US citizen in terms of applying to MD school.
I am an PR, and I had no trouble getting accepted to my state school. For other schools, I haven't heard any news other than rejections, but I believe this is due to my own short comings in comparison to other strong applicants.
Main problem faced by international applicants is their ability to pay for med school since they are less likely to be eligiable for loans, which PR's have access to as American citizens do.
Therefore, there should be no difference between PR and Citizen.
Also, I emailed a question to an admissions office regarding this matter and was told that I would be treated same as American citizen.