European banks aren't any better off. For the sake of my readers who aren't aware of European banks' exposure to Greek debt, Germany's leaders are very aware of the disastrous consequences a Greek default would have on their banks' viability. Find a European bank whose solvency isn't threatened by sovereign debt defaults and you'll be the luckiest investor in the world, until three seconds later when some hedge fund arbitrages the alpha out of that share price.
There are many more reasons not to trust large banks. I've mentioned enough to give me a reason not to invest in them for now.
Full disclosure: No positions in bank stocks at this time.