Are you forgetting that there was a bank run on IndyMac bank, which was also 'protected' by the FDIC?
Evidently, FDIC protection no longer is an adequate insurance against the risk of a bank run. One reason may be that the FDIC itself is in danger of running out of money. Which is why they are raising the fees on all banks for deposit insurance, a move that has angered many small and medium-sized banks that had nothing to do with this financial catastrophe. [Higher FDIC insurance fees will naturally cut into their profits, perhaps by a very considerable margin.]
Besides, bank runs are not the only risk subsumed within the phrase 'counter-party risks'. Has not the justification for the bailouts of Bear Stearns and AIG (and etc.) all along been that if these firms were allowed to fail, that the consequence would be severe knock-on effects throughout the entire financial system? [Of course it has.] And that fear would seem to be justified to some extent by the extreme credit crunch and financial panic which followed the bankruptcy of Lehman Brothers, which WAS allowed to fail.
This is what happens when you get financial firms that are 'too big to fail'. They are too big to fail because they are too inter-connected with all the other gigantic financial firms.
Think of it as a house of cards, for that is what it is.