Funnily enough, I agree with all of that (wot you said), and am happy to take responsibility for my own safety irrespective of FCO advice. Unfortunately the type of person we want to see visiting Turkey wont - if the FCO say dont go, they wont.
So I suppose your question is "do we, as regular travellers to Turkey know better than the FCO?". Maybe we do, maybe we don't - but the problem is that the FCO always err on the side of caution and it is their view that insurers go by.
One thing I do know is that if the FCO advise against travel to Turkey/Istanbul and I have a meeting scheduled at the office then I wont be missing it over a travel advisory. I don't think I'll be hanging about places like Taksim Square, but will still travel.
JF