Two "natural" births in hospital (2008 and 2011). Actually both in a midwife led birthing centre within the hospital.
In my case I think this was because:
Things I could control:
I was keen to have an intervention-free birth if possible.
I had prepared a bit (NCT classes the first time, this fantastic book called Birth Skills by Juju Sundin the second time). Actually I think that book was the single biggest factor in equipping me with skills which meant I could manage the pain and therefore not beg for an epidural.
I felt I could cope with the pain (just!). Although I'm not sure whether this counts as something I couldn't necessarily control!
I was happy with and supported by my birth partner.
Things I couldn't control:
The babies were in the best position, I went into labour naturally, almost on my due dates, I have no known medical issues at all which might affect birth.
The labours progressed normally with no problems on my part or the babies' parts.
So a healthy dose of luck too.
I'm not sure if a supportive midwife would be top of my list of things which helped me have a natural labour; I was so focused on dealing with the pain that I pretty much had no idea who was in the room at any one time. The midwives only piped up when necessary (eg to help me push, to suggest a position change), which was fine with me. I suppose some more cautious midwives would have been concerned that pushing with DD1 took 1hr 40mins, and I assume that it was because I had a good, well-trained midwife who was able to correctly assess that both me and the baby were coping that meant they didn't suggest any interventions.
Agree with others that not having a natural birth is not necessarily because "they" didn't "give" you one - there are many possible reasons for a birth with interventions beyond bad midwifery forcing interventions on you...