Hmmm. Given that choice, they might decide they'd rather give their money to German banks than to Greek civil servants. What happens then?
Greece defaults. And that almost certainly means that Greece exits the euro.
It's the growth thing again. If Greece defaults, nobody will loan them any money. That means huge cutbacks, which means the economy will tank, which means even more cutbacks, etc. The traditional way out of this spiral is a massive devaluation of your currency. But Greece doesn't have a currency. It has the euro*.
So if they want their economy to grow again, they have to (a) default, (b) exit the euro and re-adopt the drachma, and (c) devalue the drachma. This will cause massive amounts of pain, but it will also make Greek exports super cheap, which will eventually revive their economy.
So why not just let that happen?
It's just too catastrophic to consider. German banks, of course, would collapse and have to be bailed out. Ditto for banks in other countries that have lots of exposure to Greek debt. But that's not the worst of it. If Greece exits the euro, it will become terrifyingly obvious that other weak countries might exit too. Portugal, Spain, and Italy are the obvious candidates. Investors, spooked at the thought of their money being stuck in a country that might exit the euro and devalue all its bank deposits, would start huge runs on banks in those countries. The ECB would have to intervene and provide liquidity without limit. It would be a disaster.
So exiting the euro can't be allowed?
But if there's no exit, there's no devaluation, and Greece is pretty much screwed forever.
Basically, ain't nobody, here or there, ever thought the good times would end. Surprise!
*And just to add, this is the reason I've been saying all along that the EU will eventually turn out to be a failure and was doomed to be so from the beginning. If you have a single currency being used by 20-odd different countries without strong central control, even the smallest of economies among them can bring the whole house of cards down.