Just thought of a possible explanation. The canon magic that protects Harry from Voldie is dependent upon him returning home. Perhaps... by carrying a chunk of his home with him, Dumbledore hopes that the charm will be extended. Or some environmental factor of the place was partly responsible for repelling the Killing Curse.
Either way (D's thinking goes), better a faint hope than none at all.
Beautiful rendition of one of my favourite parts! Although, after he said that, for some strange reason I was expecting Harry to say: 'I'll treasure it always." ...It's the only thing I thought you COULD say in those circumstances.