There's a lot of info on this forum to answer your questions thoroughly, you just have to read through it.
"I think the perception is that yes, DO students can and have an advantage in getting into PMR residencies because they have more musculoskeletal training and their philosophy in Osteopathic medicine is preferred for the PMR specialty. Is that true???"
As a DO I don't think there is any such perception as what you state nor is the osteopathic philosophy preferred over allopathic medicine. Most people who match are MD's, and because more people are now applying to PM&R, it is even more competitive to get a spot as a DO student. I think the real perception is that almost all DO's will loose most of their osteopathic skills by the time they complete years 3 and 4 of medical school and complete an ACGME internship. Also, DO schools typically don't have any faculty that are physiatrist and there are only a couple DO PM&R residencies. If you want to go into PM&R I would really work on making my application stronger than the MD students.