Let's pretend that the policy holder didn't actually have any insurance cover at all (simply because that makes things easier to explain!):
If someone else has a legitimate claim against him for compensation he's then obliged to pay the claim in full HIMSELF.
If he's taken the precaution of getting some insurance cover, he can then turn to the insurer and say "Right, pay up, mate!"
However if that cover doesn't pay out the full amount (because of an 'excess' clause), it's still HIS responsibility to ensure that the claimant receives the full amount due. (The claimant can't be bound by any terms of a contract that he wasn't a party to).
So it's the POLICYHOLDER who must meet the excess.