I paste the information received by email from a very big OTA; i think this can explains why sometimes is not possible to find the same fares found on ITA!
The carrier below, Turkish is one of several airline carriers (LAN, TAM, Brussels, Copa, China Eastern, China Southern, Ethiopian Airways, Emirates, Ethiad, Hainan Airways, Jet Airways, Korean Airlines, Singapor Airlines, South African Airways, TACA, Virgin, etc.) that do not update all third party sites, in "real-time".
Please understand, the airfares we display are provided directly by the airline providers. For the airlines above, that information is "uploaded" on a scheduled intervals. This scheduling by the airline can sometimes result in a lapse between our display and "current real-time" availability. Unfortunately, as the fare/schedule information we display is provided directly by the airline operator, we are not able to "tweak" any data.
Regrettably, until Turkish has updated information for all points, including ITA, the "current" associated fare/schedule may not be available when the electronic systems "check" the airline direct feed.
Please know, we have encouraged our airline providers to improve fare/load frequency. Unfortunately, many international carriers have remained with the usual practice of interval updates. We do apologize for this inconvenience.
I have also forwarded the rate/load issue below to our operational group, in hopes they will be able to request Turkish update their fare and availability information. However, we do not have “authority” to “force” suppliers to take immediate action.
Thank you for bringing this continuing issue to our attention. We will once again escalate an appeal to Turkish for better fare information for our mutual customers.