Denouement (2 Jan 2017)
The OP returned to advise on the outcome. Here's his comment...
so I'm in turkey now. There was no formalities at the airport at all.
The IO didn't ask anything about the X on my passport. He just looked
at it. Stamped my passport and winked. And I went through. Call me
lucky but that's how you're supposed to travel. So it doesn't matter
whether u have a 'X' from the UK. It does not deter u from visiting
other countries. So it's just the UK that are so paranoid
In short, the OP breezed past the official. A great outcome with the bottom line that a UK refusal stamp did not alarm the Turkish border official. This type of mobility has the side effect of mitigating UKVI's response in the future. None of the OP's experience contradicts the original answer, so it's left intact.
You were refused entry at the UK border and then refused for UK entry clearance, so you have two indications in your passport. You want to travel to Turkey as a visa-free national and you are having anxiety about what will happen...
To begin, you will be in the official's discretionary zone. I.e., he has discretion that can play in your favour or against you.
Will I have a problem at the Turkey immigration in regards to the UK
If they see the one or two refusal indicators, they will certainly follow up with some questions. This is the time to remember that virtually all interaction with border officials is governed by personal impact and articulation skills. You will have to think how to respond. It is also a textbook example of where mock interviews in advance can be especially helpful.
Should I explain the truth or insert some white lie?
Long proven experience informs us that they have experience in assessing the response to awkward questions. They are expecting you to waffle and hedge. They will watch for you to break eye contact and shift nervously etc etc. The optimal strategy is to be delightfully candid, charmingly so. Again, personal impact will dictate how things go when a person's situation is in the discretionary zone. Your role is to help the officer do his job and you should acquit yourself of this onus in a transparent and streamlined way.
To be clear about it: If you play cat-and-mouse you will lose. If you shift blame on to your uncle or whatever you will lose. If you say that British IO's are stupid you will lose. Remember that lots of Turkish border officials are initially trained in the UK (also in Prague) and continue to take advanced courses in the UK and they totally know what provokes a UK removal.
I have a valid visa-free passport, statement of account of 6 months
and email of hotel confirmation as proof for visitation. Will that be
No, it's not sufficient. You should bring in hand luggage all of the items you used to apply for entry clearance, not just bank statements and hotel confirms. Stuff like employment contract, who your friends are etc etc. Your stuff should be well organised and easily accessible. Once again, mock interviews can be helpful.
therefore they do not share the database containing my UK entry
This type of concern is relevant only for people with something to hide. It's against our site ethos to be supportive for those wanting to hide something. Hopefully that means it's irrelevant for you also.
Geographically Turkey falls under Asia (just a small part under
Europe) shouldn't it be easier?
No. Turkey is an accession candidate for the EU. It means their national aspirations and national identity is allied with Europe's. Allegedly. Politically your mileage may vary, but at the border diligent people will treat the occasion as entering a European country.
Side note: you wrote: "...as advised by the IO...". Generally ignore what IO's advise you. During a removal situation their job is to get you out of the UK with a minimum of fuss and bother. They will tell you anything. They will promise the sun, moon, and stars if it keeps you quiet and orderly. Yes, you should apply for entry clearance, but they made it sound like a mechanical formality and you would have no problems. I know that line quite well, it gets you satisfied that everything will turn out OK. It's not a mechanical formality. Honestly, in a removal situation, just ignore their 'advice'.