The latest TIME article on the subject repeats the #3 assertion and says:
And we all know how rabidly pro-Bush CNN/Time-Warner is 
Time's bias is towards profits, so they do have an incentive to blow up this story as it makes their reporting seem more interesting.
Pay close attention to what Condolezza Rice was actually saying in her May 4 meeting with the Australian foreign minister:
"I think that over the next couple of days we will be able to describe that this is a truly significant arrest. This is, we believe, a kind of -- one of those important field generals in the al-Qaida organization."
No mention of 3rd in command. If she'd known he was 3rd in command, don't you think she would have mentioned it? At that point the former national security advisor was not even able to describe the arrest as "truly significant". She also describes him as "one of those important field generals." Clearly more in line with the description of him as a middle-level official. Yet the U.S. press, including Time, seems not to care.
Classic "appeal to ignorance"--you are saying that Rice didn't confirm the "number 3" claim and therefore the number 3 claim is false. LBJ never denied that he had Kennedy shot, therefore LBJ planned the assassination.
The CNN article from that day also does not characterize al-Libbi as "number 3"; he is only called a "senior" member. The reason for this may be explained in the TIME article I linked above:
Regardless of which story is true, it is clear that the U.S. was not willing to confirm al-Libbi's rank until well after the story broke. This is easily explained by a desire not to say too much too soon. There is no need to construct an elaborate conspiracy to explain it.
