I can't speak for Greece, but Italy is a really BAD example of a "naturally arisen" national identity. In fact the (now second party) Northern League's sole purpose until Matteo Salvini was to split Northen Italy from the south.
Source: British person living in Northern Italy with many friends from the South.
That was the agenda, then of course there are a lot of declinations the whole thing took. Like, as an example, members and sustainer of the Northern League considering the people from the south as "not Italians", derogatorily addressing them as "terroni" and so forth.
Then along came Salvini, who switched the focus from the south of Italy to the refugees, making them the enemy now. And the rest is pretty much in the daily news.
So no, sir, you did not overstate it.