I consider my birthing natural - but was given 'gas' because I couldn't help pushing, but I wasn't fully dilated. I don't think any gas was turned on (or if it was, it was minimal) but it just helped me refocus so I didn't push...
my mw did this for me too, as DD was posterior and I wanted to push at 6cm. Other than that, I had no drugs with DD, but she was taken off me quite quickly for oxygen as she was flat, and i did have a managed 3rd stage, but it was still a very empowering birth in my head as it was long and difficult and I still managed it without drugs or intervention (and I was pushing for 2.5 hours!) I had SROM with DD too.

DS felt a lot more natural, apart from having a canuula for ABs, but I was left to just let labour start in its own time (I had SROM 24hours before anything happened) and then because the labour and delivery suites were busy, I was left to get on with things in an antenatal room - noone buzzing around, just me and hubby until he realised I was in transistion. I was actually only in delivery for 10minutes until DS was born, and I was able to stay in my preferred position of standing during pushing. Again, I had a managed 3rd stage.

The recovery after DS's birth was alot quicker than DD, but it was a much quicker labour and pushing stage, and I didn't have any stitching.

So probably not natural, but natural enough for me, and definately empowering as I got to labour my way both times.