The paper seems to say that coins are transferred by signing the receiver's public key with the sender's keys. Then the receiver has to use that same "verified" public key to transfer the coins to someone else. Since the public key is connectible to an identity by the person who originally sent the coins, this is a problem.

I could be wrong about how this works, though. How do you think it works?

I understand public-key cryptography.

Look at the diagram in section 2 of the BitCoin paper. For owner 1 to send coins to owner 2, he needs to know owner 2's public key in order to create a hash and sign it. To receive payment, owner 3 needs that same public key to verify that it has been signed by owner 1.