This doesn't really say much unless we also know how the AES key itself is derived.
If you don't have two-step authentication on, then Apple's password reset is based on asking some security questions and sending an e-mail challenge. Even if they actually derived the key from your security question answers (unlikely), that's the kind of thing law enforcement would have no trouble cracking. More likely, the whole authentication system simply returns true or false, and the key is stored in some separate place -- perhaps more secure than a random hard drive in the datacenter, but still somewhere where Apple can get it if forced.
If you do have two-step authentication enabled, Apple's docs imply that it is impossible to recover your account without at least two of:
* Your password.
* Your "recovery key" -- a secret that they give you and instruct you to print out and keep somewhere.
* Your phone (or some other device that can generate one-time codes).
They say that if you can't produce two of these then all your data is lost and you'll need to create a new Apple ID. This implies that they might indeed store your data encrypted by an AES key which is in turn stored encrypted in two different ways: once with your password, and once with your recovery key. Thus it would actually be impossible to recover your data without one of these, and Apple doesn't store either one on their servers, therefore Apple would not be able to produce your data for law enforcement.
That said, I would be very surprised (and impressed) if Apple actually does this. Consider that this would prevent their services from doing any offline processing of your data at all -- a compromise few product designers would be willing to make for a security guarantee that almost no user actually understands. More likely, the language in the documentation is a matter of policy -- Apple refuses to recover your account simply because that's the only way to guarantee that social engineering is impossible, not because they are technically incapable.
And anyway, even if your data is stored encrypted at rest with a key that is actually derived from your password, there's nothing stopping law enforcement from demanding that Apple intercept your password (or the key itself) next time you log in. That's basically what they did with Lavabit, after all.
(Things I think about while working on sandstorm.io...)