A lot of the info we have on MH has come from her parents, not directly from LE. In her blog, MH's mother says that she was given the autopsy report on her daughter. I believe she also mentions seeing what was left of her daughter.
I don't know how the coroner was able to determine that MH was raped ,and that she was brutally beaten. We don't know if this is a conclusion that MH's mother has made, or it is an official verdict from the coroner. Since the remains were skeletal, I don't know how LE could have gotten semen samples from her body...but MH might have been left with some shreds of clothing or something that had semen on it.
Semen is not the only thing that has DNA on it. Hair, skin, blood do as well. So we don't know what LE was using to get what matches at this point. We do know that a good DNA swab was done so that an optimal sample is now being used from JM to run matches. From what I understand, the forensic analyses were done second hand before, likely from the car, clothing, apartment of JM's to get those preliminary links. Links and direct matches are not the same, either.
The other thing is that cause of death for MH has not been released. I read that from the condition of a throat bone, a coroner can establish death by strangulation many times even from skeletal remains, so I am guessing that was the case for MH. The woman raped in Fairfax was injured from a strangulation attempt along with the rape, but survived because the rapist did not finish here off due the someone coming to investigate. And those two cases are linked by DNA, as we know.