I've always assumed that "specialized health sciences" referred to things like nursing, pharmacy, PT, etc. so no, I wouldn't think public health would fall under this category.
I'm assuming that you're asking in regards to AAMC table 17 (
https://www.aamc.org/download/321496/data/factstablea17.pdf), which shows that specialized health science majors tend to have lower MCAT scores. If what you're really asking is whether being a public health major will decrease your chance of doing well on the MCAT, the answer is no. It's up to you to prepare for the MCAT by doing well in your prereqs and devoting plenty of time to studying. You could major in art history and still get a great MCAT score and get into med school.
My guess as to why "specialized health science" majors don't score as highly on the MCAT is because their coursework is often different than the science courses geared toward premeds. (i.e. chemistry courses offered specifically for nursing students)
OP, as people on this site have now told you in SEVERAL different threads:
1) Major in whatever you want! Medical schools do not care. (Stop obsessing and posting the same thread over and over expecting a different response.)
2) Get the highest GPA you're capable of.
3) Study, study, study for the MCAT and crush it.