First off, your finger needs to make contact with the sensor. I know you don't press on it. Your finger does have to come in contact with the sensor though for it to work. Even the instructions you posted says, "relax and lightly place your finger" on the heart rate monitor. If you don't think it needs to, try it and you will find that it won't work unless your finger comes in contact. I have used the sensor since getting the phone. More than once!!
There is a strip of the case that separates the camera lens and the auto focus lens that works for the heart rate sensor. What I am trying to convey is I "cannot" get my finger into the opening to touch the sensor because of the strip and was just trying to pass on this info to someone that is thinking about purchasing the case so that they will know and won't be disappointed like I was.
Take a moment and go back and read my original post... I essentially said the same thing...