I'm a 6th year MD-PhD student (MD 1-2, PhD 1-4) finishing a PhD in Health Policy and Management.
A couple of thoughts:
1. Contrary to what's been posted above, I've found NIH receptive to funding the work I do, as have many of my fellow public health MD-PhD students. I was carried by our program's MSTP grant in my first year of medical school, and received an F30 on my initial submission to NHLBI. During my first two years of graduate school, I was also carried on my advisor's R01 from NIA. The key is career goal. If your stated goal is to be a policymaker (e.g., to run a state Medicaid program) then no, NIH isn't going to fund that. If you're interested in doing a mix of applied research and methodology development, NIH is happy to fund. AHRQ and now PCORI are other sources of funding.
2. It's definitely true that a portion of the work I do could be done by somebody with an MPH or similar degree (as is true about the workload of most physician and PhD scientists), but there are other aspects of my work that could not be done without study beyond the MPH, whether via independent study, PhD, post-doc, etc. Again, it depends on career goal.
3. I'm curious what PhD program you have in mind as a comparator when you deem the Michigan HPM curriculum as being "kind of lax". Michigan is a highly respected program. At least at my institution, the coursework requirements of Public Health PhD programs are much more extensive than those of biomedical PhD programs. The tradeoff is that completion of the dissertation project generally goes much more quickly in public health than biomedical; in general, these tend to balance out to roughly equal time to graduation.
4. "Anyone can understand what you mean if you are working on figuring out whether Big Macs cause heart attacks, whereas if you are studying the conformational dynamics of beta-actin pleated sheets in high shear environments, you sound like a genius."
Economists, sociologists, political scientists, operations researchers, etc. (all of whom are under the HPM umbrella) are quite capable of producing impressive-sounding jargon.
5. Yes, you should ask programs whether they're willing to consider such a degree before applying. However, they're not as rare as other commenters who applied 10+ years ago think they are. I'm on adcom at my school, and we are almost always competing for the public health students we want with other institutions. Search other posts for lists.