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Consider a toxic asset held by Citibank with a face value of $1 million, but with zero probability of any payout and therefore with a zero market value. An outside bidder would not pay anything for such an asset. All of the previous articles consider the case of true outside bidders.
Suppose, however, that Citibank itself sets up a Citibank Public-Private Investment Fund (CPPIF) under the Geithner-Summers plan. The CPPIF will bid the full face value of $1 million for the worthless asset, because it can borrow $850K from the FDIC, and get $75K from the Treasury, to make the purchase! Citibank will only have to put in $75K of the total.
Citibank thereby receives $1 million for the worthless asset, while the CPPIF ends up with an utterly worthless asset against $850K in debt to the FDIC. The CPPIF therefore quietly declares bankruptcy, while Citibank walks away with a cool $1 million. Citibank's net profit on the transaction is $925K (remember that the bank invested $75K in the CPPIF) and the taxpayers lose $925K. Since the total of toxic assets in the banking system exceeds $1 trillion, and perhaps reaches $2-3 trillion, the amount of potential rip-off in the Geithner-Summers plan is unconscionably large.
...And the gaming of the system doesn't have to be as crude as Citibank setting up its own CPPIF. There are lots of ways that it can do this indirectly, for example, buying assets of other banks which in turn buy Citi's assets. Or other stakeholders in Citi, such as groups of bondholders and shareholders, could do the same.