All of these examples involve some kind of two party trust, but not one requires both parties trust a third. Not even the verification of the blockchain.
Trusted third parties are very useful when trading with someone you don't trust. One person trusts the trading administrator enough to deposit bitcoins and the other person trusts a payment processor such as Liberty Reserve or Pecunix to provide proof to the trading administrator that the payment occurred and he trust the trading site administrator that he'll accept proof of payment. Both traders have to trust the trading site and the payment processor, both third parties, but they don't need to trust each other.