Yes, but (especially) Greece and Italy aren't known for their stability in recent years.

As mentioned above, those are EU passport. If Italy becomes unstable you can still go to Germany or Austria for example.

If the situation in Italy actually got bad, the EU would suspend Italy's membership or at least many EU rights (such as freedom of movement) very quickly. As usual, everyone likes their neighbors until they don't.

If you're rich you're leaving Italy way before that, and member states wouldn't suspend rights of Italians already in their country.

As stated in the article, by getting a passport from any EU nation, you are free to travel to/live in/work in any EU country.

Neither Greece or Italy seem to be on the brink of a new civil war, nor do they have more owned guns than inhabitants (AFAIK). If anything, instability in these countries mostly means more opportunities for people with lots of money.

They don't have to live in Greece. The passport gets you access to the EU.