To be fair, the BBC in a more detailed report on their website says that Greek Air Traffic Controllers planned only a 3 or 4 hour walkout today, to show support for the general protest against austerity measures demanded by financial institutions affected if Greece were to go bankrupt and drop out of the Euro. I have a hard time working up any sympathy for French Bankers.
Also on the Beeb website is a photo of a large sign that proclaims "Greek Airspace is Not for Sale!" Is it possible that privatisation has been suggested for Greek ATC?