I've been in the public health sector for a few years and it seems that anyone serious about their career has a PhD, not necessarily in public health, but related fields. The only people I know who hold only an MPH are basically career middle managers (grant coordinators or program managers included), who incidentally, all have husbands with big jobs in high paying fields like finance or law. I don't know if this is the norm, but seems to be correlated. The MPH falls within the 'helping professions' (if it can be seen as a professional degree at all) similar to social work. There is also this 'me too' approach to primary care that i can't totally explain, as though an MPH has value to bring into primary care decision making.
It mostly distills to grant work in practice. Research is a different story, but one does not need the quasi-specialization of the MPH to perform statistical research. Although an understanding of epidemiology would help, biostats doesn't differ from statistics for the behavioral sciences and is less rigorous than a pure statistics degree, which would give you additional options. Point being, unless the letters after your name matter, then anyone with a technical MBA, MPPM, stats, even an MS in research psychology, would give you the same skillset needed for PH research. That's the other thing -- all the research PH people I know have technical masters degrees other than MPH.
All that said, I think there is some value for doctors, particularly those who have spent their lives exclusively inside the clinical setting, to have a look at the overview of public health concepts, but it's like comparing a social work degree to an MD or PhD in the natural sciences.