Pretty emotive subject!
For me, a gourmet burger may have pink middle if made freshly from steak cuts, but burgers by nature are made from everything. If I have ground offal that isnt cooked through that for me isnt only a health risk but a big turn off. Even mince, dont trust it. By increasing the surface area of food you increase risk of food bourne nasties.
Living in Britain you'll be lucky if its beef in your burger and not horse! We also tend to be over cautious when it comes food due to things such as the BSE scare in the 90's. So no I am not joking, it's a combination of things that puts me off eating pink burgers.