It's not a lot of use proving you're MR X unless burnside had already accepted that MR X owned the account in question.
That's why the guarantor signs a statement of ownership and not a statement of identity (although such a letter would naturally include your identity). It means you provide proof of your ownership i.e. you sign a message with the withdrawal address. I completely agree that without accepting that MR X owns the account in question it would be ludicrous to turn it over to him simply because he proves he has an identity.
I wouldn't be surprised if ignoring such a letter would open you to some kind of civil suit in most parts of the world.