I also refused to labour on my back or give brth that way...much to the horror of my student midwife when I started to push (without her telling me I could) and moved onto the floor 
However, if you are happier and more comfy on the bed, why not?
I found being on the bed very painful, as was standing up.
I was on a birth ball for my labours and delivered ds1 squatting and ds2 kneeling.
Both VERY quick pushing stage (about 6-8 pushed each) but I tore with both.
Really felt for Donna - she was very brave.
Dont like the heart condition woman - sorry. She is behaving like a spoilt teenager.