Now I don't want to cause any problems here but I have to say this; I'm pretty sure that she IS holding them correctly. However, I'm basing this off of what I was taught during my own lessons that I took ten years ago. Anyway, regardless of how she's holding onto the reins, the pictures from this photo shoot are really cool and, in my opinion, well done.
No, she is holding them the wrong way around...the straps attached to the bit should be going through the gap in her fingers at the bottom and coming out of the top, but I think different cultures have different ways of holding the reins. However, I learnt to ride in England, so she should be holding them in this (^^) way.
However, the picture makes up for this slight fault XD