I asked Nishul about this. If I own a credit default swap (let's say I'm Party B in the graphic above), and I want to get out of my position, am I likely to assign that CDS to someone else, or am I likely instead to simply enter into a new insurance contract which is equal and opposite to the first one?
If you're worried about counterparty risk and the NYT's problem, then there's good news and bad news. The bad news is that I am indeed most likely to assign the contract I've got, rather then piling up a bunch of nominally-offsetting trades. The good news, however, is that hedge funds and other buyers of CDS almost never trade directly with each other. If I assign the contract, I'm going to be assigning it to a dealer.
What this means is that you're very unlikely to get a long chain of assignments as illustrated by the NYT. Normally the chain stops at Party C: the dealer that the original counterparty assigned his contract to. This doesn't increase counterparty risk, it reduces it, since dealers generally don't worry about each others' counterparty risk. It's much more likely a hedge fund will go bust than that a broker-dealer will go bust and be unable to fulfill its commitments, especially since broker-dealer CDS desks generally don't make big directional bets.
But what about those CDS auctions I was so worried about? Surely anybody can wind up buying a contract in one of those? Actually, no. The auctions held by Markit and Creditex are the auctions which happen after an event of default - they're called "credit event auctions" - and they exist to set a cash-settlement price on the value of the CDS. The CDS themselves don't actually change hands.
Obviously, counterparty risk in the CDS market is non-zero. But the fact that you can assigning your CDS to a third party doesn't in practice exacerbate it, and neither does the existence of these auctions.