The political favoritism factor really isn't a factor in the papal decision to reject Henry's case, rather it was that Henry's argument was obviously doomed.
Why?
Henry asserted that the impediment was a matter of Divine Law and no earthly power could dispense it, ever. This was a dumb argument. It was asking the Pope not only to limit his own authority and power forever, but to also repudiate his predecessor (and declare the Church to have taught error), and to invalidate all marriages given such a dispensation, including other royal/noble marriages. Henry was ill advised on this matter. Other, much less problematic arguments were available, yet Henry put forward the most problematic argument possible. There was never any possibility of the declaration of nullity being granted on those grounds. It is as if no one in England bothered to think through the implications and ask the question: would any sane ruler make a ruling that undermines their own authority and limits their own power?