I think the reason that Korean and Chinese banks might be hesitant to borrow from the Fed is that once you take money from Uncle Sam, you are going to have inspectors from the Federal Reserve pouring over the books of the parent company. (Which is also why stand alone investment banks might be skittish about getting money from the Fed.)
Also, unlike the Korean and Chinese central banks, the Fed is unlikely to loan money to a foreign bank which is actually insolvent. The problem with the Chinese banks wasn’t a liquidity issue but a solvency issue, and I think the same was true for the Korean banks. If you need recapitalization then a loan from the Fed is not going to help you.
The really interesting thing is to see how much power the Fed is amassing at the expense of the SEC. The big battle is Bernanke versus Cox, and Bernanke is winning this. The other interesting thing to watch is whether this will be the end of the independent investment bank. Also, it does seem interesting that the financial system of the US is starting to look a lot like the Chinese financial system with four really huge banks that are basically controlled by the central bank, which exercises its power by the fact that it can print money, whereas private shareholders can’t.