When the usual methods of password recovery fail, then things get problematic.
Keep in mind that the easier it is to convince suport to reset/recover a password that is not your own the easier it is for a criminal to fool support into handing that account over.
After Apple was burned by this once, publicly and embarassingly, they've gotten pretty strick in their requirements. Combine this with their public stance on security and they'd rather take the bad will of someone not getting access to their account than the even worse publicity of handing that account over to someone who shouldn't have it.
Criminals asside, even giving this info to the wrong (not legally empowered) family member could get them sued. And because it's Apple it would be as public and as embarasing as the media could make it.
Security is always a tradeoff between convinience and safety. And someone is always on the wrong side of that tradeoff no matter how hard you try.
None of this helps you, of course. But it might make you feel a bit better to understand why Apple's doing this. It's not about not carring. It's about having to choose what you care about the most, and knowing that no matter what you choose, someones going to be mad at you.