Paulson is correct in that nobody's (yet) lost a penny from an FDIC insured account.
However, with the level of fear out there, it might be prudent to have a larger than normal amount of cash on hand to meet your normal needs. Your money may be safe in the bank, but the bank could be closed for some days or weeks if people start running them and accessing the cash might be more problematic than normal.
I'm not saying to develop a Y2K level of paranoia, but money can always be replaced in the account pretty quick and easy with little harm done.