Wow. This seems seriously daft and lacking completely in common sense. I too have needle phobia. I have fainted when having blood drawn.
The trick is to explain that you have needle phobia to the doctor or nurse before having blood taken. In my case I cannot watch the needle going in. I need to lie down and not be sitting upright as I almost feel like I am being attacked or a sense of claustrophobia in that moment. Once it's all over take a few minutes or even a quarter of an hour to recompose yourself and that's it. To have a condition attached to your medical because of this is just nutsy cuckoo.