It is true. If Citibank or any of the big four failed, the FDIC does not have enough money, or legal authority, to prevent its collapse. Even the head of the FDIC (a brilliant and straight-shooting woman) thought so in the midst of the crisis:
http://curiouscapitalist.blogs.time...-citigroup-could-the-fdic-actually-take-over/
The problem with thinking like that is that bigger banks, generally, allow credit to flow more freely. (for better or for worse) Bigger banks, by way of their larger capitalization, are willing to take more risks with borrowers, which in turn helps generate economic activity. Your line of thought would result in smaller institutions that would not take risks and would hinder economic activity.
Of course there is a risk that their collapse could endanger the US economy, but that risk does NOT outweigh the benefits. While it might be easy and convenient to say 'bust them up', that's the lazy answer. It doesn't solve the problem and most certainly would NOT result in a better situation than the bank being large. There are trade-offs, and your 'solution' decimates the positive aspects of large banks in favor of some hazy, ill-defined benefits of smaller institutions.
The answer, which you curiously did not mention, and the RIGHT answer, is more stringent regulations on the types of risks banks like Citibank are allowed to take. The SIZE of the bank is not the issue; its what the bank does with its assets and is allowed to do with borrowers. If there is a bank that holds that much wealth in its coffers, the government should force it to temper the kinds of risks it takes; not all risks are bad, just like not all of them are good. But, quite simply, a bigger bank is able to take risks that smaller banks cannot, and absorb losses should those risks not be productive. THAT alone is enough reason to keep bigger banks around. (with some proper regulation, of course)