My guess is the OP said they had a single entry visa, and it seemed that was used up when they went into VCE. Had they flown non-stop to ATH from anywhere in Italy they would have been fine and no exit visa would have been stamped as it was most likely @ VCE.

By flying to IST even to connect, the passport was stamped with the exit visa from the EU so the person would need another EU visa to renter in any EU country.

In regards to IST even US passport holders need a visa to enter, but US citizens can get it just before exiting, which is not the case with all Passports. Id guess whatever Country the OPs wife is a citizen of doesnt have the visa on arrival option

Now this may start to be a problem to US citizens as well if the EU starts requiring US citizens to get a visa. If that goes into affect then those entering and exiting the EU as the OP wanted to do might just get us into the same situation as the OP found himself.

I know some folks who ran into this problem when visiting Vietnam and booked a side trip to Cambodia before heading to Hanoi+.Once they entered and left Nam that was the end of that visa they got and werent allowed back into Nam since they didnt have an unused visa