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If I'm reading their specs correctly, if A manages to break the chip she could generate duplicate transactions for the full value stored on the chip to B and C and D (and E and F and...).
But she wouldn't be able to double-spend the same funds to B, because B's chip is able to detect that attempted double-spend.
Eventually, I assume the Mint would figure out that the same funds were spent at B and C and D and... etc, just like the Mint eventually figures out when a lot of counterfeit paper notes are being spent in a particular area. And I imagine they'd deal with it the same way, interviewing merchants to ask them if they have a record of who made a transaction at a particular time, etc.
And assuming B/C/D/... did nothing wrong I bet the Mint honors all of the the A -> B/C/D/... transactions, so B/C/D/... don't lose any money. The Mint eats the loss (it just shows up as inflation in the money supply, so really EVERYBODY pays for the fraud), and if the problem gets large enough they declare version 1.0 of their chips obsolete and come out with a New and More Secure version.
It all looks pretty nifty to me, I hope it is a big success; it could be a great way to buy Bitcoins (non-reversible, cash-like...).