Harvard is also a 9-month program geared toward individuals who have completed or who are in the process of completing a doctoral-level degree. http://www.hsph.harvard.edu/mph/questions.html
It is possible to complete an MPH in a year if you try to get all of your requirements completed in that time (taking summer courses, extra credits, etc.). Most often, it takes 1.5 to 2 years, depending on background. Some programs waive up to 12 credits for students with a medical or other doctoral-level degree. Don't forget that in addition to taking courses in public health, most programs require students to apply their knowledge in the form of a thesis, practicum, or both. This is why it usually takes longer than a year to complete an MPH.