I think that OBs attending homebirths used to be more common. My brother and I were born at home, an my mother had an OB and midwife at home. They all worked together in a homebirth practice. This was in the 70's and early 80's. Neither of them still practice homebirth, if they practice at all.
EMT's do NOT have skills to attend to labor and birthing. They are trained to handle an emergency hospital transport, and learn very little about how to handle the nuances of birthing. My brother is an EMT, and it was funny to hear about his "birth training". Most OB who are new on the scene or in the middle of their practice's life, often do not have the full skills to handle natural childbirth. Training is usaully concerned with observation, diagnosis and intervention. OBs are certainly trained to use technology. I think you can still find older OBs who are skilled at handling different presentation and a wide variety of birth scenarios where they are able to help the women remain on the path of a natural childbirth. I would love to hear otherwise, but this is my understanding. Additionally, docs in other fields I would not consider qualified to attend a birth based on their MD title.
Though, people certainly can learn...