Yes, an osteopath can diagnose. And yes, you have to go through medical training to be a doctor, kevbone. Medical Doctors go to medical school, osteopaths go to osteopathic school, chiropractors go to chiropractic school, eye doctors go to ophthalmic school (i think), dentists go to dental school etc etc etc. And archenemy is correct. You will get a good diagnosis seeing an osteopath, a doctor of physical therapy (i think they can legally diagnose in some states), or a chiropractor.
I would see a chiropractor for garden variety muscluoskeletal stuff - even up to mild-moderate neurological damage -just like I'd see the family doc for garden variety colds and prescriptions (like hypertension or high cholesterol). I'd see an osteopath if there was major trauma. I'd see a PT for rehab from major trauma. Just the way I'd go about it. And sirwoofalot comment unfortunately rings true, just like I feel what happens when I used to go to my medical doc for my musculoskeletal complaints.