To whom else would "him" refer? Absent other context, there's no other plausible referrent. While surrounding context might create ambiguity, such ambiguity is generally no worse than in cases where a subject or object exists to which the pronoun may or may not refer.
Consider the sentence "Bob often polishes his shoes". Whose shoes does Bob polish?
Now imagine the previous sentence read "Joe likes to visit his friend Bob." Now whose shoes does Bob polish?
Now imagine the following sentence reads "This is in stark contrast to Joe's former friend Steve, whose shoes so badly needed polish that they looked balder than Homer Simpson."
Note that while it would be possible to change the ambiguous possessive to "his own" to make clear whose whose shoes Bob was polishing, it would change the 'feel' of the sentence in an awkward way.