You're right, he's not referring to the cliff-like withdrawal of funding that may result from downgrades, but rather the relatively gradual deterioration in the capitalization of Greek banks.
However, I don't think this is actually that big of a deal. I don't know about other types of collateral, but for guvvies the recent moves are a) not that large in terms of all-in bond PVs; b) are accompanied by lower main refi rate expectations, which softens the blow a little.
Generally, he's correct, but there's so much priced in, it's hard to see how much further such deterioration one can expect on the funding side. The big problem, in my view, are the non-linear effects, such as depositor runs, impact of ratings actions on bond indices, etc...