Not sure about the Persia/Turkey link (I would just assume migrations into Eastern Europe/Russia, but I'm ignorant on any specific migrations), but keep the following in mind:
1. Missing branches multiply quickly.
2. Assumptions are dangerous.
So, when you (or anyone - not picking on you) say your grandfather was "Pure Italian," does this mean you have every branch of his ancestry documented for (say) the past 10 generations? I'm not saying all of his ancestors aren't from the region of Italy, but time after time when discussing their DNA results, people say "but I'm 50% this" or "but my grandfather came from a long line of..." and what they're thinking of is the paper trail they know and/or the cultural identity of more recent ancestors. They're forgetting about all of the ancestors they don't know and what those people contributed.
Few people have a full tree at 10 generations out (that's over a thousand ancestors), so all kinds of unexpected ethnicities, surnames, and locations may/will show up. Of course, it's not just those missing branches leading to surprises, either - there's also the matter of which traits you in particular have inherited. Maybe your DNA input from your mom just really favours your maternal grandmother. :)
And, in the end, there's also the issue of how the testing company chooses to label things, plus incomplete reporting from some who have done the test. (Those early BYU testers who reported their four-generation pedigree when the gave samples - did they really know enough with a four-generation chart to say where their people were from?)
Ancestry says our ethnicity results are likely to change, so I wouldn't really give the ethnicity much credence (fun as it is to ponder). :)