The ISDA is the final arbiter who determines whether a default is a "credit event" which would trigger insurance pay-outs over failed bonds. Bonds are insured by credit default swaps (CDSs) and other "over the counter" (OTC) derivatives, which are unregulated, off market. The value of OTC contracts (open positions) is at least $700 trillion. The value exceeded one quadrillion dollars before the valuation methods were altered, improving some balance sheets. Although most of those positions would cancel out, some do not because some contracts and obligations disappeared with Lehman's failure. Some "sides of the bargain" no longer exist. Even with only a small imbalance in OTC positions, the scale of the effects of a credit event could be in the trillions of dollars.
There would be strong pressure from G20 and other governments, and from those large financial institutions which are "too big to fail", and from central banks, for the ISDA to determine that no Greek default "credit event" has occurred, in spite of Greek sovereign debt holders suffering losses because of Greece's failure to honour their debt obligations.
I thank Jim Sinclair for drawing this to my attention.