I'm afraid I've never used Face Time (or Skype with a webcam as I don't have one) but that does seem really odd. Isn't it possible to change the camera direction like one does on a phone camera? I assume it has a picture in picture?

I always download my photos to my desktop, my phone isn't cloud connected. In case of phone loss I don't want a lot of images on it and I prefer to use the memory for music and audio