All top PH schools (UNC, Harvard, Hopkins, Mailman) are very competitive. Most have around 5%-10% acceptance rate for the PhD/DrPH. For example, Mailman's DrPH in Global Health Leadership admits ~5 out of more than 60 applicants. UNC's leadership DrPH requires 10+ years of experience. The applicant pool as one would guess for UNC is much smaller but in no way less competitive. No school admits 50 people unless if it is an online program.
From speaking to a few people, I think the this year's intake for Harvard's DrPH will be 15. The plan is to increase the class size gradually up to 25. I doubt Harvard will fully fund the entire DrPH class. Professional qualifications rarely provide full scholarships.
changetheworld: you have very impressive stats. My only worry is whether the CEO of Genetech and Deans of the schools spent enough time to write a good reference, as these guys are super busy.