Watch Lawrence O’Donnell (who is no friend of Paul’s) debunk the AP story.
It turns out that those first class flights that Paul was accused of taking on the tax payers dime were actually upgrades that he purchased using his frequent flier miles. Paul buys all his tickets at the standard coach rates. The tickets he buys are refundable which means they are slightly more expensive, but because the congress never sticks to its schedule, it is a necessity that the tickets be refundable rather than the cheaper non-refundable advance tickets.
So in short, the AP story was a flat out smear that has no basis in reality at all.
Don’t hold your breath waiting for a retraction.