The issue is expected loss. No one knew what is the expected loss in a crisis. This is why some of the Lehman debt holders actually made money from the bankruptcy. This is why TARP actually made money. It is because there is a substantial difference in asset price while in crisis and not in crisis. The asset price is what is making the bank solvent.
Of course, the central bank (unless you are locked into a monetary union of course) can lend freely during a crisis. However, it must also be careful as to not trigger inflation or worse yet cause people to lose faith with your currency. There is also moral hazard as well but that's more of a soft issue.
The bigger issue is what happens if your bank liability is many times larger than your countries GDP. This was the case with Iceland or Britain. Then you can't print enough money to make your bank whole.
The issue here is that we know Greece is not as competitive in exports as Germany. So what can Greece do to run a trade surplus while in a common currency union with Germany? They are not able to depreciate their currency. They are not allowed to put up tariffs either. Also, where does the German do with their export surplus. They don't just hide it under the mattress. German banks is also looking for a outlet, however, Greece is not allowed to implement capital control to block the inflow. So the only alternative is to out compete Germany or some other Euro-zone countries (but this just substitute Greece for some other PIGS).
The key here is that for everyone in the world, the trade surplus and deficit must sum to zero. So someone has to run a trade deficit if German/Japan/China wants to run a trade surplus. German now wants the entire eurozone to run a trade surplus which means someone else must run a even bigger trade deficit.
BTW, it is in theory possible for Greece to run a government budget surplus but a trade deficit. This would mean that the private sector is loading up on the debt. Even in this case, the private sector is really the banks which has to be backstopped by the government anyway. So bank debt is just another form of government debt.
I guess you have to define what a solvent bank is. I don't think any bank can handle a sustained run given their liability duration mismatch. So I am not sure what do you mean that you can't create a panic. Its always possible to have runs just not very easily.
The financial crisis showed that bank liabilities are really liabilities of the country that the bank incorporates in. So in case of Ireland, Greece, Iceland, it is up to the country to step up and backstop their banks. If a country can not, then you will have panic on a bank. And in order for a country to be able to backstop their banks, the debt of the country must be credible.
Of course, the central bank (unless you are locked into a monetary union of course) can lend freely during a crisis. However, it must also be careful as to not trigger inflation or worse yet cause people to lose faith with your currency. There is also moral hazard as well but that's more of a soft issue.
The bigger issue is what happens if your bank liability is many times larger than your countries GDP. This was the case with Iceland or Britain. Then you can't print enough money to make your bank whole.