To stay with the OP and not wander off into Tred Barta land:
My objection would be more to the TV presentation than to the actions.
That is, as an archer, I'd just as soon not be the target of a wounded lion or buffalo during those last moments before the arrow's wound is actually effective in causing death. The old "stop is more important than kill" deal. So, yeah, a post-mortem would establish whether or not the arrow's damage would have been a clean bleed-out and kill, but the rifle would have ensured a stop.
IOW, if this indeed were the thinking of the scenario, it should have been explained up front in the TV presentation.
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