The whole idea behind that was that Qhorin Halfhand knew Jon would never be accepted by the Wildlings unless he demonstrated that he was willing to turn on his fellow rangers. In the book it's not quite as drawn out, the two of them get stuck in a cave with the wildlings outside, and (and I can't remember the details) they end up fighting to the death in much the same fashion. Qhorin knew he was going to die, and by sacrificing himself he gave Jon more credit in the Wildlings' eyes than Jon had before. I wouldn't expect them to trust Jon fully yet either, but it's enough that they're willing to let him into their encampment.
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