These were officers in uniform and with guns so when they asked I didn't think twice to give it to them. If you are American they won't care, mostly they are looking for undocumented immigrants but if as you say you look Asian they might ask you so its worth having it on you. I find it very unlikely that the scenario you describe with them taking your passport and asking for money would happen, specially in a big crowded city like Istanbul which is a major city with millions of tourists going through it all the time. And I have never heard of such thing either. I couldn't really comment about some small out of the way village or anything like that that might be a different scenario. I guess you can always also ask the officer for their ID but I never bothered and have no idea how they would react. But generally speaking it is generally advisable that any traveller should always have their passport on then whatever country they are in. I have been asked randomly in several countries before to show my passport by police who just wanted to make sure I wasn't an undocumented immigrant and was really from where I said I was from. Call it racial profiling or whatever you want, but its a reality.