I agree with this statement to a certain extent. For the purpose of applying to medical school, I believe just being considered for the DO degree is the first priority. However, if you are really interested in public health, than an MPH is a great addition. However, depending on what you want to do with your MPH, it is better to apply to an MPH program that is accredited by CEPH. As far as I know, most DO/MPH programs are not accredited by CEPH.
If you just want to have an MPH just for the sake of having an MPH to understand public health better, than go for it, but if you really want it make something out of it I would suggest applying to accredited MPH programs. There are some MPH programs that you can do in 1 year if you are willing to take a year off, say after 2nd year, or you could apply to part-time MPH programs. A great program is Johns Hopkins where you do a majority of your courses online but spend a few months on their campus.
At any rate, good luck