Greek default versus Euro exit
As far as I recall, you're dead on: they don't have to. The contracts don't allow for "some countries kicking others out of the Euro Zone", they never envisioned this scenario when writing them.

On the other side, Greece can, and should, leave on its own. Sharing the currency is hurting them economically, the only reason they're not is that the continuous inflow of loans is preferred over leaving the zone. But if Greece really defaults, I don't think there will be any more lending in the short run. And then really there is no reason for Greece to stay.