It wasn't their mistake, it was his mistake. You can't just register an account, then hand it off to someone else and not be at least partially responsible for what happens through that account.
If Apple didn't want to avoid the bad PR, they could just terminate their business relationship permanently, and they'd be in the right, even morally, since it was Kapeli who violated the trust.
It's unclear whether he registered it himself, but it doesn't matter, since according to the terms of service:
"You can choose from the payment methods presented during your membership purchase. If you are paying by credit card and enrolling as an individual, you must use your own credit card to complete your purchase. If you do not, your enrollment will be delayed and you will be asked for a copy of your government-issued photo identification."
At least he did not use the same name. The two accounts use different names, otherwise apple would mention it because it's a huge evidence that the accounts are linked :)
It says if you do not pay by credit card, we want your photo ID, or at least it's ambiguous.
Again, it's unclear under whose name the account really was registered, but if he went through the trouble of sending in photo ID, Kapeli would probably mention that as to further exonerate him of any mistakes.
They're be asking for photo id of the actual account holder, i.e. the relative, in lieu of id via CC account. And given that Apple was willing to reinstate his account, Kapeli is already exonerated.
Apple was willing to reinstate the account only under the condition that Kapeli admits there was a mistake on his part, so clearly that doesn't exonerate him from having signed up for an account for a third party under his identity. This is Apple's position and I would expect they have designed their terms so that this position holds up.
If Apple didn't want to avoid the bad PR, they could just terminate their business relationship permanently, and they'd be in the right, even morally, since it was Kapeli who violated the trust.