State medical licensing is a different ballgame altogether. Every state has a slightly different set of rules and documentation requirements. I don't think a non-accredited residency affects licensure in a majority of states, so long as you can prove you were in a residency program, but I could be wrong. But having a license is worthless if you can't find a place to work because your training background is sketchy.
Not to put words in JAD's mouth, but I think he was trying to point out that most med students know that there is a 'path' to full licensure and practice, and that most med students would realize that a non-accredited program is not on the well traveled path, but one filled with unknown obstacles. Thus, most med students would try to avoid this path altogether; med students are very leery of something that is clearly very different from the rest. While they want a residency, they also realize that accredited is better than non-accredited.
I think most MS4s realize very quickly that accreditation is important, because:
1. the vast majority of programs that they are researching via FREIDA and other sites are accredited and advertise this.
2. non-accredited programs will 'look' different to them and set off warning bells--for example, really high turnover rates, residents who seem sketchy, program details are sketchy, too-good-to-be-true promises, etc. etc.
3. when seeking advice from others, are told to avoid these programs