If Greece left the euro zone, it would have to leave the EU
"The treaties indeed confirm what we have been saying here: the treaty doesn’t foresee an exit from the euro zone without exiting the EU, so indeed that is the current situation."
-European Commission spokeswoman Karolina Kottova
Article 50 of the EU treaty: “Any member state may decide to withdraw from the union in accordance with its own constitutional requirements.”
Translation: countries check into the EZ motel but they don’t check out!
Also see the FT where it explains:
The [EU] treaties do include a sort of emergency clause that allows the European Commission, the EU’s executive arm, to make proposals to deal with extraordinary events that are a threat to the single currency. So it could probably use this as a basis to draft a Greek exit, if necessary. As with all EU matters, the process would not be immediate. The other 26 member states would have to unanimously approve, as well as the European Parliament.
Thanks to a clause in the Lisbon treaty, which came into force in 2009, Greece could take a more radical approach and opt to leave the EU altogether. (This clause was added at the behest of the UK, to prove to its eurosceptic voters that the bloc was not a straitjacket that could never be removed). In this case, Greece would require only majority approval from other member states.
So, never say never. The European lawyers are resourceful. After all, some in the Bundesbank were saying way back in 2010 that the Troika bailouts were unconstitutional and they figured out a way to do them anyway. I am sure that they could figure out a way to get Greece out of the euro zone without it’s having to exit the EU. But, the official line has to be tough lest periphery governments start to get ideas.