I remember reading a thead (or three) a while back that divided opinion about how people put their bras on. It was pretty much 50/50 that some fastened them behind their backs and some fastened them under boob then twisted round. I am in the latter camp and it did puzzle me how it's possible to do up your bra behind your back... 
However, I was at an aerobics class a few days ago, and the instructor asked us all to link our own hands behind our backs and connect them (if that makes sense!) which I couldn't do - neither could a lot of people (I noted as I was stood at the back observing!). We were all people of differing statures and weights (so not a 'long arm' issue) - so I wondered if the world's back bra fasteners are the same people that can connect their hands behind their backs?!