Extract private RSA key from USB cryptographic token using Bardou et al. attack (variant of "million message attack")
Their attack does not recover the private key.  Instead, it gives the attacker a way to decrypt an arbitrary ciphertext of the attacker's choosing.  (This is not the same thing.)

If the attacker has a ciphertext $c$, the attacker can query the hardware device tens of thousands of times and then based upon the responses, deduce what the decryption of $c$ is.  If the next day the attacker runs across another ciphertext $c'$ that he wants to decrypt, he needs to issue another tens of thousands of queries to the hardware device.  That's pretty bad -- but it's not as bad as revealing the private key. 

So, the answer to your question is: no, their attack does not reveal the private key.

(I think all of this is already covered in the links you mentioned in the question, so I'm not sure whether I understood what you were asking.)