Transit area in European airports is the area that you reach when getting out of an international (extra-Schengen) flight or, when going to your (extra-Schengen) flight, you reach after passing through immigration. When in there, you are considered to be "outside" the country. Turkey is nor a member of the EU and is not a signatory of the Schengen agreement. In other words, you need no visa for the transit area, as you were correctly informed by the Turkish Dept of Foreign Affairs. My guess is that the consular officer at NYC wrongly thought of the situation in the US. At any rate, you will not pass immigration and they will not ask for your passport, but you'd have to have your BC already, otherwise I take back most of the above...