Does it matter where you go to medical school? There are many reports out there that say you should not go get an MBA or JD unless you are going for the Top 5 or Top 10 schools respectively. The rationale is that the lost salary and tuition does not make up for the expected NPV difference (get a professional degree vs. do not get a professional degree).

I have never heard this about medical schools. It seems reasonable to assume that most patients do not inquire about their doctor's alma mater and that there is a lot of standardization in the final board exam. Also, most medical schools have an extremely low dropout/failure rate (&lt;5%). However, there is huge variability among the selectivity of medical schools,  ranging from an average undergraduate GPA and MCAT score of 3.35 and 20 respectively, all the way up to 3.89 and 38.

What advantages does a Duke M.D. have over a Marshall University M.D.? Am I correct in assuming that the average salary distribution over all US medical schools is relatively flat?
I disagree. There are very little differences between medical schools so long as you do well on your STEP I through STEP III exams. Basically what really matters is how you rank compared to the national average. 
I have interviewed residency candidates from around the country-their alma mater means very little to me. Their STEP scores and extracurricular activities matter as well as their personal statements. Don't worry about medical school ranking-just worry about Step exam scores-that will really help you get into any residency program you want.