My reply was to the comment "any bank in the world...", so I'm giving a valid example where a person can obtain a CC without being a resident or generating income at the country.

And...Cyprus is not Italy, so I'm not sure how much of your experience applies to the process with Alpha bank Cyprus.

Edit: I've followed the link you've provided, and in the "Useful information" section it seems that it works as debit card:
https://goo.gl/p5xAfw
"
Useful information about you card

You can pay off your card balance in the following ways:

By direct debit from your bank account held with Alpha Bank
At any Alpha Bank branch
At any Alpha Bank ATM in Cyprus by cash or cheque deposit or by direct debit from your bank account
Via the Internet, by using the Alpha Express Banking Electronic Services provided you maintain an Alpha Bank account
"